A Continuum Damage Mechanics-based Piecewise Fatigue Damage Model for Fatigue Life Prediction of Fiber-Reinforced Laminated Composites

Document Type : Original Article

Authors

1 Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, Iran

2 Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran

Abstract

The purpose of this study is to define a piecewise fatigue damage model (PFDM) for the prediction of damage in composite laminates under cyclic loading based on the continuum damage mechanics (CDM) model. Assuming that damage in fiber-reinforced plastic structures accumulates nonlinearly, a piecewise degradation growth function is defined and coupled with CDM and micromechanics approaches. The model divides the damage behavior of fiber, matrix, and fiber/matrix debonding at the ply scale, into three different stages. For generality, a fully multi-stage damage formulation on a single-ply level is employed. The unknown parameters of the PFDM are estimated according to obtained experimental data of damage mechanisms associated with the composites laminate under cyclic loading. To predict multidirectional composite laminates' fatigue life, the proposed model was implemented in Abaqus software by the subroutine. In a validation against experimental data on carbon fiber reinforced material, the model proves to provide a good numerical approximation of the damage during the fatigue loading. The results reveal that by considering the multi-stage process in stiffness reduction, the proposed model can estimate the fatigue life of composite laminate under multiaxial cyclic loading conditions more accurately than the similar model in the literature.

Keywords

References

1.     Asyraf, M., Ishak, M.R., Sapuan, S., Yidris, N., Shahroze, R., Johari, A., Rafidah, M. and Ilyas, R., "Creep test rig for cantilever beam: Fundamentals, prospects and present views", Journal of Mechanical Engineering and Sciences,  Vol. 14, No. 2, (2020), 6869-6887, doi: 10.15282/jmes.14.2.2020.26.0538.
2.     Asyraf, M., Ishak, M., Sapuan, S., Yidris, N., Ilyas, R., Rafidah, M. and Razman, M., "Potential application of green composites for cross arm component in transmission tower: A brief review", International Journal of Polymer Science,  Vol. 2020, (2020), doi: 10.1155/2020/8878300.
3.     Asyraf, M., Ishak, M., Sapuan, S., Yidris, N. and Ilyas, R., "Woods and composites cantilever beam: A comprehensive review of experimental and numerical creep methodologies", Journal of Materials Research and Technology,  Vol. 9, No. 3, (2020), 6759-6776, doi: 10.1016/j.jmrt.2020.01.013.
4.     Mohd Nurazzi, N., Muhammad Asyraf, M., Khalina, A., Abdullah, N., Sabaruddin, F.A., Kamarudin, S.H., Ahmad, S., Mahat, A.M., Lee, C.L. and Aisyah, H., "Fabrication, functionalization, and application of carbon nanotube-reinforced polymer composite: An overview", Polymers,  Vol. 13, No. 7, (2021), 1047, doi: 10.3390/polym13071047.
5.     Ha, K., "Innovative blade trailing edge flap design concept using flexible torsion bar and worm drive", HighTech and Innovation Journal,  Vol. 1, No. 3, (2020), 101-106, doi: 10.28991/HIJ-2020-01-03-01.
6.     Battistelli, D., Ferreira, D.P., Costa, S., Santulli, C. and Fangueiro, R., "Conductive thermoplastic starch (tps) composite filled with waste iron filings", Emerging Science Journal,  Vol. 4, No. 3, (2020), 136-147, doi: 10.28991/esj-2020-01218.
7.     Asyraf, M., Ishak, M., Sapuan, S., Yidris, N., Ilyas, R., Rafidah, M. and Razman, M., "Evaluation of design and simulation of creep test rig for full-scale crossarm structure", Advances in Civil Engineering,  Vol. 2020, (2020), doi: 10.1155/2020/6980918.
8.     Alsubari, S., Zuhri, M., Sapuan, S., Ishak, M., Ilyas, R. and Asyraf, M., "Potential of natural fiber reinforced polymer composites in sandwich structures: A review on its mechanical properties", Polymers,  Vol. 13, No. 3, (2021), 423, doi: 10.3390/polym13030423.
9.     Nurazzi, N., Asyraf, M., Khalina, A., Abdullah, N., Aisyah, H., Rafiqah, S., Sabaruddin, F., Kamarudin, S., Norrrahim, M. and Ilyas, R., "A review on natural fiber reinforced polymer composite for bullet proof and ballistic applications", Polymers,  Vol. 13, No. 4, (2021), 646, doi: 10.3390/polym13040646.
10.   Wu, Q. and Wang, Y., "Experimental detection of composite delamination damage based on ultrasonic infrared thermography", International Journal of Engineering, Transactions B: Applications, Vol. 27, No. 11, (2014), 1723-1730. doi: 10.5829/idosi.ije.2014.27.11b.10
11.   Mohammad Zaheri, F. and Majzoubi, G., "Numerical and experimental study of ballistic response of kevlar fabric and kevlar/epoxy composite", International Journal of Engineering, Transactions B: Applications, Vol. 30, No. 5, (2017), 791-799. doi: 10.5829/idosi.ije.2017.30.05b.20
12.   Jhanji, K. and PVN, L., "Influence of circular and square cut-outs on fiber glass/epoxy composite laminate under tensile loading", International Journal of Engineering, Transactions A: Basics,  Vol. 31, No. 1, (2018), 104-109. doi: 10.5829/ije.2018.31.01a.15
13.   Askaripour, K. and Fadaee, M., "Diagnosis of delaminated composites using post-processed strain measurements under impact loading", International Journal of Engineering, Transactions A: Basics,  Vol. 32, No. 1, (2019), 54-61. doi: 10.5829/ije.2019.32.01a.07
14.   Rastegarian, S. and Sharifi, A., "An investigation on the correlation of inter-story drift and performance objectives in conventional rc frames", Emerging Science Journal,  Vol. 2, No. 3, (2018), 140-147, doi: 10.28991/esj-2018-01137.
15.   Fazelabdolabadi, B. and Golestan, M.H., "Towards bayesian quantification of permeability in micro-scale porous structures–the database of micro networks", HighTech and Innovation Journal,  Vol. 1, No. 4, (2020), 148-160, doi: 10.28991/HIJ-2020-01-04-02.
16.   Hashin, Z. and Rotem, A., "A fatigue failure criterion for fiber reinforced materials", Journal of Composite Materials,  Vol. 7, No. 4, (1973), 448-464, doi: 10.1177/002199837300700404.
17.   Vassilopoulos, A.P., Manshadi, B.D. and Keller, T., "Influence of the constant life diagram formulation on the fatigue life prediction of composite materials", International Journal of Fatigue,  Vol. 32, No. 4, (2010), 659-669, doi: 10.1016/j.ijfatigue.2009.09.008.
18.   Whitworth, H., "A stiffness degradation model for composite laminates under fatigue loading", Composite Structures,  Vol. 40, No. 2, (1997), 95-101, doi: 10.1016/S0263-8223(97)00142-6.
19.   Zhang, Y., Vassilopoulos, A.P. and Keller, T., "Stiffness degradation and fatigue life prediction of adhesively-bonded joints for fiber-reinforced polymer composites", International Journal of Fatigue,  Vol. 30, No. 10-11, (2008), 1813-1820, doi: 10.1016/j.ijfatigue.2008.02.007.
20.   Shokrieh, M.M. and Lessard, L.B., "Progressive fatigue damage modeling of composite materials, part i: Modeling", Journal of Composite Materials,  Vol. 34, No. 13, (2000), 1056-1080, doi: 10.1177/002199830003401301.
21.   Philippidis, T. and Passipoularidis, V., "Residual strength after fatigue in composites: Theory vs. Experiment", International Journal of Fatigue,  Vol. 29, No. 12, (2007), 2104-2116, doi: 10.1016/j.ijfatigue.2007.01.019.
22.   Reifsnider, K.L. and Stinchcomb, W., A critical-element model of the residual strength and life of fatigue-loaded composite coupons, in Composite materials: Fatigue and fracture. 1986, ASTM International.
23.   Pineda, E.J., Bednarcyk, B.A. and Arnold, S.M., "Validated progressive damage analysis of simple polymer matrix composite laminates exhibiting matrix microdamage: Comparing macromechanics and micromechanics", Composites Science and Technology,  Vol. 133, (2016), 184-191, doi: 10.1016/j.compscitech.2016.07.018.
24.   Krüger, H. and Rolfes, R., "A physically based fatigue damage model for fibre-reinforced plastics under plane loading", International Journal of Fatigue,  Vol. 70, (2015), 241-251, doi: 10.1016/j.ijfatigue.2014.09.023.
25.   Vassilopoulos, A.P., Fatigue life prediction of composites and composite structures, Woodhead publishing,  (2019).
26.   Fawaz, Z. and Ellyin, F., "Fatigue failure model for fibre-reinforced materials under general loading conditions", Journal of Composite Materials,  Vol. 28, No. 15, (1994), 1432-1451, doi: 10.1177/002199839402801503.
27.   Shokrieh, M.M. and Lessard, L.B., "Progressive fatigue damage modeling of composite materials, part ii: Material characterization and model verification", Journal of Composite Materials,  Vol. 34, No. 13, (2000), 1081-1116, doi: 10.1177/002199830003401302.
28.   K Ahmaditabar, K., Ahmadi, I. and Hashemi, M., "Stiffness prediction of beech wood flour polypropylene composite by using proper fiber orientation distribution function", International Journal of Engineering, Transactions A: Basics, Vol. 30, No. 4, (2017), 582-590. doi: 10.5829/idosi.ije.2017.30.04a.17
29.   Bagheri, R., Peason, R. and Marouf, B., "Modeling of stiffening and strengthening in nano-layered silicate/epoxy (research note)", International Journal of Engineering, Transactions A: Basics, Vol. 30, No. 1, (2017), 93-100. doi: 10.5829/idosi.ije.2017.30.01a.12
30.   Ogi, K., Yashiro, S., Takahashi, M. and Ogihara, S., "A probabilistic static fatigue model for transverse cracking in cfrp cross-ply laminates", Composites Science and Technology,  Vol. 69, No. 3-4, (2009), 469-476, doi: 10.1016/j.compscitech.2008.11.023.
31.   McCartney, L., "Energy methods for fatigue damage modelling of laminates", Composites Science and Technology,  Vol. 68, No. 13, (2008), 2601-2615, doi: 10.1016/j.compscitech.2008.04.044.
32.   Zhang, H. and Minnetyan, L., "Variational analysis of transverse cracking and local delamination in [θm/90n] s laminates", International Journal of Solids and Structures,  Vol. 43, No. 22-23, (2006), 7061-7081, doi: 10.1016/j.ijsolstr.2006.03.004.
33.   Rafiee, R. and Elasmi, F., "Theoretical modeling of fatigue phenomenon in composite pipes", Composite Structures,  Vol. 161, (2017), 256-263, doi: 10.1016/j.compstruct.2016.11.054.
34.   Ladeveze, P., "A damage computational method for composite structures", Computers & Structures,  Vol. 44, No. 1-2, (1992), 79-87, doi: 10.1016/0045-7949(92)90226-P.
35.   Allix, O. and Ladevèze, P., "Interlaminar interface modelling for the prediction of delamination", Composite Structures,  Vol. 22, No. 4, (1992), 235-242, doi: 10.1016/0263-8223(92)90060-P.
36.   Payan, J. and Hochard, C., "Damage modelling of laminated carbon/epoxy composites under static and fatigue loadings", International Journal of Fatigue,  Vol. 24, No. 2-4, (2002), 299-306, doi: 10.1016/S0142-1123(01)00085-8.
37.   Xiong, J. and Shenoi, R., "A two-stage theory on fatigue damage and life prediction of composites", Composites Science and Technology,  Vol. 64, No. 9, (2004), 1331-1343, doi: 10.1016/j.compscitech.2003.10.006.
38.   Kawai, M. and Honda, N., "Off-axis fatigue behavior of a carbon/epoxy cross-ply laminate and predictions considering inelasticity and in situ strength of embedded plies", International Journal of Fatigue,  Vol. 30, No. 10-11, (2008), 1743-1755, doi: 10.1016/j.ijfatigue.2008.02.009.
39.   Shi, W., Hu, W., Zhang, M. and Meng, Q., "A damage mechanics model for fatigue life prediction of fiber reinforced polymer composite lamina", Acta Mechanica Solida Sinica,  Vol. 24, No. 5, (2011), 399-410, doi: 10.1016/S0894-9166(11)60040-2.
40.   Zhang, X. and Zhao, J., "Applied fatigue damage mechanics of metallic structural members", National Defence Industry Press, Beijing, (1998).
41.   Movaghghar, A. and Lvov, G., "An energy model for fatigue life prediction of composite materials using continuum damage mechanics", in Applied Mechanics and Materials, Trans Tech Publ. Vol. 110, (2012), 1353-1360, doi: 10.4028/www.scientific.net/AMM.110-116.1353.
42.   Salimi-Majd, D., Helmi, M. and Mohammadi, B., "Damage growth prediction of unidirectional layered composites under cyclic loading using an energy based model", Modares Mechanical Engineering,  Vol. 15, No. 7, (2015), 173-180.
43.   Mohammadi, B., Fazlali, B. and Salimi-Majd, D., "Development of a continuum damage model for fatigue life prediction of laminated composites", Composites Part A: Applied Science and Manufacturing,  Vol. 93, (2017), 163-176, doi: 10.1016/j.compositesa.2016.11.021.
44.   Mahmoudi, A., Mohammadi, B. and Hosseini‐Toudeshky, H., "Damage behaviour of laminated composites during fatigue loading", Fatigue & Fracture of Engineering Materials & Structures,  Vol. 43, No. 4, (2019), doi: 10.1111/ffe.13152.
45.   Hohe, J., Gall, M., Fliegener, S. and Hamid, Z.M.A., "A continuum damage mechanics model for fatigue and degradation of fiber reinforced materials", Journal of Composite Materials,  Vol. 54, No. 21, (2020), 0021998320904142, doi: 10.1177/0021998320904142.
 
 
 
 
 
 
 
 
 
 
 
 
 
46.   Naderi, M. and Khonsari, M., "Thermodynamic analysis of fatigue failure in a composite laminate", Mechanics of Materials,  Vol. 46, (2012), 113-122, doi: 10.1016/j.mechmat.2011.12.003.
47.   Naderi, M. and Khonsari, M., "On the role of damage energy in the fatigue degradation characterization of a composite laminate", Composites Part B: Engineering,  Vol. 45, No. 1, (2013), 528-537, doi: 10.1016/j.compositesb.2012.07.028.
48.   Mohammadi, B. and Mahmoudi, A., "Developing a new model to predict the fatigue life of cross-ply laminates using coupled cdm-entropy generation approach", Theoretical and Applied Fracture Mechanics,  Vol. 95, (2018), 18-27, doi: 10.1016/j.tafmec.2018.02.012.
49.   Mahmoudi, A. and Mohammadi, B., "On the evaluation of damage-entropy model in cross-ply laminated composites", Engineering Fracture Mechanics,  Vol. 219, (2019), 106626, doi: 10.1016/j.engfracmech.2019.106626.
50.   Emeka, A.E., Chukwuemeka, A.J. and Okwudili, M.B., "Deformation behaviour of erodible soil stabilized with cement and quarry dust", Emerging Science Journal,  Vol. 2, No. 6, (2018), 383-387, doi: 10.28991/esj-2018-01157.
51.   Nadjafi, M. and Gholami, P., "Reliability analysis of notched plates under anisotropic damage based on uniaxial loading using continuum damage mechanics approach", International Journal of Engineering, Transactions A: Basics, Vol. 34, No. 01, (2021), 253-262, doi:10.5829/ije.2021.34.01a.28.
52.   Choupani, N. and Heydari, M.H., "A new comparative method to evaluate the fracture properties of laminated composite", International Journal of Engineering, Transactions C: Aspects, Vol. 27, No. 6, (2014), 991-1004. doi:10.5829/idosi.ije.2014.27.06c.18
53.   Ladeveze, P. and LeDantec, E., "Damage modelling of the elementary ply for laminated composites", Composites Science and Technology,  Vol. 43, No. 3, (1992), 257-267, doi: 10.1016/0266-3538(92)90097-M.
54.   Huang, Z.-M., "Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model", Composites Part A: Applied Science and Manufacturing,  Vol. 32, No. 2, (2001), 143-172, doi: 10.1016/S1359-835X(00)00142-1.
55.   Shokrieh, M.M. and Lessard, L.B., "Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments—ii. Experimental evaluation", International Journal of Fatigue,  Vol. 19, No. 3, (1997), 209-217, doi: 10.1016/S0142-1123(96)00068-0.
56.   Yang, S., Stiffness degradation of composite laminates. 1987, George Washington Univ., Washington, DC (USA).
57.   Naderi, M. and Maligno, A., "Fatigue life prediction of carbon/epoxy laminates by stochastic numerical simulation", Composite Structures,  Vol. 94, No. 3, (2012), 1052-1059, doi: 10.1016/j.compstruct.2011.11.013.
58.   Dunn, O.J. and Clark, V.A., Applied statistics: Analysis of variance end regression. 1987, John Wiley & Sons.
International Journal of Engineering
Volume 34, Issue 6
TRANSACTIONS C: Aspects
June 2021
Pages 1512-1522

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