Cover
Vol. 25 No. 1 (2025)

Published: September 9, 2025

Pages: 92-111

Review Article

Composite Materials Under Fatigue Loading: General Review

Abstract

Advanced applications, such as aircraft manufacturing, require sophisticated materials. Composite materials are among these advanced materials and offer several advantages, including high strength and low weight. Given that these applications experience repeated loading, studying fatigue in composite materials is essential. This paper provides a comprehensive review of fatigue failure in composite materials, focusing on the types of fatigue loads, the characteristics of composite materials, and the damage mechanisms. Additionally, we discuss modelling and simulation techniques to understand fatigue behavior and the standards necessary for conducting fatigue failure testing in composite materials. The study of fatigue in composite materials is diverse, reflecting the materials' complexity, which varies across scales. Due to composite materials' heterogeneity, numerical modelling can be challenging. It often requires numerous constants that change with various factors, which can only be determined through experimental test. As a result, studying fatigue in composite materials can be costly.

References

  1. A. P. Vassilopoulos, “The history of fiber-reinforced polymer composite laminate fatigue,” International Journal of Fatigue, vol. 134, p. 105512, 2020.
  2. H. Malekinejad, R. J. Carbas, A. Akhavan-Safar, E. A. Marques, F. Castro Sousa, and L. F. da Silva, “Enhancing fatigue life and strength of adhesively bonded composite joints: A comprehensive review,” Materials, vol. 16, no. 19, p. 6468, 2023.
  3. W. Brostow and H. E. H. Lobland, Materials: introduction and applications. John Wiley & Sons, 2016.
  4. K. Kiefer, “Simulation of high-cycle fatigue-driven delamination in composites using a cohesive zone model,” Imperial College London, 2014. https://core.ac.uk/download/pdf/76989726.pdf
  5. D. K. Rajak, D. D. Pagar, R. Kumar, and C. I. Pruncu, “Recent progress of reinforcement materials: a comprehensive overview of composite materials,” Journal of Materials Research and Technology, vol. 8, no. 6, pp. 6354-6374, 2019.
  6. M. Zaludek, S. Rusnakova, M. Kubisova, O. Bilek, and K. Karvanis, “Fatigue life of thermoset composite materials,” IOP Conference Series: Materials Science and Engineering, vol. 726, no. 1, p. 012016, 2020.
  7. G. G. Lozano, A. Tiwari, C. Turner, and S. Astwood, “A review on design for manufacture of variable stiffness composite laminates,” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 230, no. 6, pp. 981-992, 2016.
  8. M. Asim, N. Saba, M. Jawaid, and M. Nasir, “Potential of natural fiber/biomass filler-reinforced polymer composites in aerospace applications,” Sustainable composites for aerospace applications, pp. 253-268, 2018.
  9. R. Hsissou, R. Seghiri, Z. Benzekri, M. Hilali, M. Rafik, and A. Elharfi, “Polymer composite materials: A comprehensive review,” Composite structures, vol. 262, p. 113640, 2021.
  10. B. Abu-Jdayil, A.-H. Mourad, W. Hittini, M. Hassan, and S. Hameedi, “Traditional, state-of-the-art and renewable thermal building insulation materials: An overview,” Construction and Building Materials, vol. 214, pp. 709-735, 2019.
  11. X. Zhang, Y. Chen, and J. Hu, “Recent advances in the development of aerospace materials,” Progress in Aerospace Sciences, vol. 97, pp. 22-34, 2018.
  12. V. Arun Prakash, J. F. Xavier, G. Ramesh, T. Maridurai, K. S. Kumar, and R. B. S. Raj, “Mechanical, thermal and fatigue behaviour of surface-treated novel Caryota urens fibre–reinforced epoxy composite,” Biomass Conversion and Biorefinery, vol. 12, no. 12, pp. 5451-5461, 2022.
  13. B. Parveez, M. Kittur, I. A. Badruddin, S. Kamangar, M. Hussien, and M. Umarfarooq, “Scientific advancements in composite materials for aircraft applications: a review,” Polymers, vol. 14, no. 22, p. 5007, 2022.
  14. M. Rafiee, F. Nitzsche, and M. Labrosse, “Dynamics, vibration and control of rotating composite beams and blades: A critical review,” Thin-Walled Structures, vol. 119, pp. 795-819, 2017.
  15. B. Wang and H. Gao, “Fibre reinforced polymer composites,” in Advances in Machining of Composite Materials: Conventional and Non-conventional Processes: Springer, pp. 15-43, 2021.
  16. G. Mustafa, A. Suleman, and C. Crawford, “Probabilistic micromechanical analysis of composite material stiffness properties for a wind turbine blade,” Composite Structures, vol. 131, pp. 905-916, 2015.
  17. M. A. Meyers and K. K. Chawla, Mechanical behavior of materials. Cambridge university press, 2008.
  18. A. Vedrtnam, “Novel method for improving fatigue behavior of carbon fiber reinforced epoxy composite,” Composites Part B: Engineering, vol. 157, pp. 305-321, 2019.
  19. N. Zohdi and R. Yang, “Material anisotropy in additively manufactured polymers and polymer composites: a review,” Polymers, vol. 13, no. 19, p. 3368, 2021.
  20. B. Harris, Fatigue in composites: science and technology of the fatigue response of fibre-reinforced plastics. Woodhead Publishing, 2003.
  21. M. Arulraj, P. Palani, and M. Sowrirajan, “Optimization of squeeze casting parameters of hybrid aluminium matrix composite using Taguchi approach,” Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, vol. 235, no. 4, pp. 1073-1081, 2021.
  22. A. Moudood, A. Rahman, A. Öchsner, M. Islam, and G. Francucci, “Flax fiber and its composites: An overview of water and moisture absorption impact on their performance,” Journal of Reinforced Plastics and Composites, vol. 38, no. 7, pp. 323-339, 2019. https://doi.org/10.1177/0731684418818893
  23. M. Balasubramanian, Composite materials and processing. CRC press Boca Raton, 2014.
  24. M. Rutkowska et al., “Homogeneity study of candidate reference material (contaminated soil) based on determination of selected metals, PCBs and PAHs,” Measurement, vol. 128, pp. 112, 2018. https://doi.org/10.1016/j.measurement.2018.06.021
  25. S. OFFLINE, Mechanical behavior of materials-engineering methods for deformation, fracture, and fatigue. Pearson, 2013.
  26. A. P. Pröll, “Fatigue Damage Models for Laminated Composite Structures/submitted by Andreas Peter Pröll,” 2017. https://epub.jku.at/obvulihs/content/titleinfo/2195445
  27. P.-Y. Mechin, V. Keryvin, J.-C. Grandidier, and D. Glehen, “An experimental protocol to measure the parameters affecting the compressive strength of CFRP with a fibre micro-buckling failure criterion,” Composite Structures, vol. 211, pp. 154-162, 2019.
  28. C. Zhao, B. Wang, and J. Xiao, “Macroscopic characterization of fiber micro-buckling and its influence on composites tensile performance,” Journal of Reinforced Plastics and Composites, vol. 36, no. 3, pp. 196-205, 2017.
  29. K. Jamroziak, M. Kosobudzki, and M. Majzner, “The concept of fatigue test of composite materials,” Vibroengineering Procedia, vol. 3, pp. 186-189, 2014. https://www.extrica.com/article/15502
  30. A. Delbariani-Nejad and A. Farrokhabadi, “A failure criterion to predict the onset of matrix cracking induced delamination in general composite laminates,” Composite Structures, vol. 235, p. 111564, 2020.
  31. Y. M. Bezzie, V. Paramasivam, S. Tilahun, and S. K. Selvaraj, “A review on failure mechanisms and analysis of multidirectional laminates,” Materials Today: Proceedings, vol. 46, pp. 73807388, 2021. https://doi.org/10.1016/j.matpr.2020.12.1121
  32. S. Eliasson, “A Framework for Fatigue Analysis of Carbon Fiber Reinforced Polymer Structures,” KTH Royal Institute of Technology, 2023. https://www.diva-portal.org/smash/record.jsf?pid=diva2:1810533
  33. R. Talreja, “Fatigue of composite materials,” Modern trends in composite laminates mechanics: Springer, pp. 281-294, 2003.
  34. I. Burhan and H. S. Kim, “SN curve models for composite materials characterisation: an evaluative review,” Journal of Composites Science, vol. 2, no. 3, p. 38, 2018.
  35. P. Alam, D. Mamalis, C. Robert, C. Floreani, and C. M. Ó. Brádaigh, “The fatigue of carbon fibre reinforced plastics-A review,” Composites Part B: Engineering, vol. 166, pp. 555-579, 2019. https://doi.org/10.1016/j.compositesb.2019.02.016
  36. S. Mortazavian and A. Fatemi, “Fatigue behavior and modeling of short fiber reinforced polymer composites: A literature review,” International Journal of Fatigue, vol. 70, pp. 297-321, 2015. https://doi.org/10.1016/j.ijfatigue.2014.10.005
  37. J. A. Pascoe, R. C. Alderliesten, and R. Benedictus, “Methods for the prediction of fatigue delamination growth in composites and adhesive bonds–a critical review,” Engineering Fracture Mechanics, vol. 112, pp. 72-96, 2013.
  38. B. L. Bak, C. Sarrado, A. Turon, and J. Costa, “Delamination under fatigue loads in composite laminates: a review on the observed phenomenology and computational methods,” Applied Mechanics Reviews, vol. 66, no. 6, p. 060803, 2014.
  39. A. Tabiei and W. Zhang, “Composite laminate delamination simulation and experiment: A review of recent development,” Applied Mechanics Reviews, vol. 70, no. 3, p. 030801, 2018.
  40. J. Deng, J. Zhou, T. Wu, Z. Liu, and Z. Wu, “Review and Assessment of Fatigue Delamination Damage of Laminated Composite Structures,” Materials, vol. 16, no. 24, p. 7677, 2023.
  41. R. Khan, R. Alderliesten, S. Badshah, and R. Benedictus, “Effect of stress ratio or mean stress on fatigue delamination growth in composites: critical review,” Composite Structures, vol. 124, pp. 214-227, 2015.
  42. X. Gao et al., “Mode I fatigue of fibre reinforced polymeric composites: a review,” Polymers, vol. 14, no. 21, p. 4558, 2022.
  43. M. T. A. Ansari, K. K. Singh, and M. S. Azam, “Fatigue damage analysis of fiber-reinforced polymer composites-A review,” Journal of Reinforced Plastics and Composites, vol. 37, no. 9, pp. 636-654, 2018. https://doi.org/10.1177/0731684418754713
  44. N. Vikram and R. Kumar, “Review on fatigue-crack growth and finite element method,” International Journal of Scientific & Engineering Research, vol. 4, no. 4, pp. 833-843, 2013.
  45. N. Post, S. Case, and J. Lesko, “Modeling the variable amplitude fatigue of composite materials: A review and evaluation of the state of the art for spectrum loading,” International Journal of Fatigue, vol. 30, no. 12, pp. 2064-2086, 2008. https://doi.org/10.1016/j.ijfatigue.2008.07.002
  46. P. K. Mallick, Materials, design and manufacturing for lightweight vehicles. Woodhead publishing, 2020.
  47. H. Mughrabi, “Microstructural mechanisms of cyclic deformation, fatigue crack initiation and early crack growth,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 373, no. 2038, p. 20140132, 2015. https://doi.org/10.1098/rsta.2014.0132
  48. S. Vethe, “Numerical simulation of fatigue crack growth,” Institutt for produktutvikling og materialer, 2012.
  49. A. Elkin, V. Gaibel, D. Dzhurinskiy, and I. Sergeichev, “A multiaxial fatigue damage model based on constant life diagrams for polymer fiber-reinforced laminates,” Polymers, vol. 14, no. 22, p. 4985, 2022. https://doi.org/10.3390/polym14224985
  50. K. F. Hasan, P. G. Horváth, and T. Alpár, “Potential fabricreinforced composites: a comprehensive review,” Journal of Materials Science, vol. 56, no. 26, pp. 14381-14415, 2021.
  51. D. D. Chung, Composite materials: science and applications. Springer Science & Business Media, 2010.
  52. M. Karahan, “Comparison of ballistic performance and energy absorption capabilities of woven and unidirectional aramid fabrics,” Textile research journal, vol. 78, no. 8, pp. 718-730, 2008. https://doi.org/10.1177/0040517508090487
  53. Z. Bergant, A. Savin, and J. Grum, “Effects of manufacturing technology on static, multi-frequency dynamic mechanical analysis and fracture energy of cross-ply and quasi-isotropic carbon/epoxy laminates,” Polymers and Polymer Composites, vol. 26, no. 5-6, pp. 358-370, 2018.
  54. A. K. Kaw, Mechanics of composite materials. CRC press, 2005.
  55. M. W. D. Nielsen, “Design of Aerospace Laminates for MultiAxis Loading and Damage Tolerance,” University of Bath, 2017.
  56. G. Guillamet, J. Costa, A. Turon, and J. Mayugo, “In search of the quasi-isotropic laminate with optimal delamination resistance under off-axis loads,” Journal of Reinforced Plastics and Composites, vol. 43, no. 7-8, pp. 440-455, 2024.
  57. C. Casavola, A. Cazzato, V. Moramarco, and C. Pappalettere, “Orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory,” Materials & design, vol. 90, pp. 453-458, 2016.
  58. C. Kohlhauser and C. Hellmich, “Determination of Poisson’s ratios in isotropic, transversely isotropic, and orthotropic materials by means of combined ultrasonic-mechanical testing of normal stiffnesses: Application to metals and wood,” European Journal of Mechanics-A/Solids, vol. 33, pp. 82-98, 2012.
  59. L. L. Vignoli, J. T. P. de Castro, and M. A. Meggiolaro, “Stress concentration issues in unidirectional laminates,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 41, no. 10, p. 462, 2019.
  60. G. Staab, Laminar composites. Butterworth-Heinemann, 2015.
  61. J. C. Halpin, Primer on composite materials analysis (Revised). Routledge, 2017.
  62. A. T. Nettles, “Basic mechanics of laminated composite plates,” 1994. https://ntrs.nasa.gov/api/citations/19950009349/downloads/19950009349.pdf
  63. C. Hwu, Mechanics of Laminated Composite Structures. CRC Press, 2024.
  64. D. Motamedi, “Nonlinear XFEM modeling of delamination in fiber reinforced composites considering uncertain fracture properties and effect of fiber bridging,” University of British Columbia, 2013.
  65. E. Randbaran, L. Dayang, R. Zahari, M. Sultan, and N. Mazlan, “Advantages and Disadvantages of Using Composite Laminates in the Industries,” Mod. Approaches Mater. Sci, vol. 32, pp. 349352, 2020. https://doi.org/10.32474/mams.2020.03.000158
  66. S. Shah, S. Karuppanan, P. Megat-Yusoff, and Z. Sajid, “Impact resistance and damage tolerance of fiber reinforced composites: A review,” Composite Structures, vol. 217, pp. 100-121, 2019.
  67. A. P. Pröll, “Fatigue Damage Models for Laminated Composite Structures/submitted by Andreas Peter Pröll,” Universität Linz, 2017. https://epub.jku.at/obvulihs/content/titleinfo/2195445
  68. A. Raimondo and A. Riccio, “Inter-laminar and intra-laminar damage evolution in composite panels with skin-stringer debonding under compression,” Composites Part B: Engineering, vol. 94, pp. 139-151, 2016.
  69. L. Retschitzegger, “Progressive Damage Simulation Methods for Laminated Composites using Abaqus/eingereicht von Lukas Retschitzegger,” 2016.
  70. M. Hameed, “Modelling Fracture and Fatigue Failure of Laminated Composites,” University of Manchester, 2019.
  71. R. Khan, R. Alderliesten, and R. Benedictus, “Two-parameter model for delamination growth under mode I fatigue loading (Part B: Model development),” Composites Part A: Applied Science and Manufacturing, vol. 65, pp. 201-210, 2014.
  72. M. Kaminski, F. Laurin, J. Maire, C. Rakotoarisoa, and E. Hémon, “Fatigue damage modeling of composite structures: the onera viewpoint,” Aerospace lab, no. 9, pp. p. 1-12, 2015.
  73. R. Talreja and J. Varna, Modeling damage, fatigue and failure of composite materials. Elsevier, 2023.
  74. J. Degrieck and and W. Van Paepegem, “Fatigue damage modeling of fibre-reinforced composite materials,” Appl. Mech. Rev., vol. 54, no. 4, pp. 279-300, 2001.
  75. N. S. Ottosen, R. Stenström, and M. Ristinmaa, “Continuum approach to high-cycle fatigue modeling,” International Journal of Fatigue, vol. 30, no. 6, pp. 996-1006, 2008.
  76. R. Mula, “A systematic methodology for fatigue analysis of machine elements with characterized dynamic loads,” Purdue University, 2019.
  77. A. D’Amore and L. Grassia, “Principal features of fatigue and residual strength of composite materials subjected to Constant Amplitude (CA) loading,” Materials, vol. 12, no. 16, p. 2586, 2019. https://doi.org/10.3390/ma12162586
  78. B. Fazlali, S. V. Lomov, and Y. Swolfs, “Fiber break model for tension-tension fatigue of unidirectional composites,” Composites Part B: Engineering, vol. 220, p. 108970, 2021.
  79. A. V. Movahedi-Rad, T. Keller, and A. P. Vassilopoulos, “Fatigue damage in angle-ply GFRP laminates under tensiontension fatigue,” International Journal of Fatigue, vol. 109, pp. 60-69, 2018.
  80. A. Pertuz, S. Díaz-Cardona, and O. A. González-Estrada, “Static and fatigue behaviour of continuous fibre reinforced thermoplastic composites manufactured by fused deposition modelling technique,” International Journal of Fatigue, vol. 130, 2020. https://doi.org/10.1016/j.ijfatigue.2019.105275
  81. C. Zhou, S. Zhou, Y. Peng, and Q. Sun, “Study on the fatigue modeling of FRP composite materials,” 2016 5th International Conference on Energy and Environmental Protection (ICEEP 2016), Atlantis Press, pp. 763-767, 2016.
  82. D. Djeghader and B. Redjel, “Fatigue life prediction of glass reinforced composite materials using Weibull distribution,” Composites Theory and Practice, vol. 19, no. 3, pp. 100-106, 2019.
  83. T. Park, M. Kim, B. Jang, J. Lee, and J. Park, “A nonlinear constant life model for the fatigue life prediction of composite structures,” Advanced Composite Materials, vol. 23, no. 4, pp. 337-350, 2014. https://doi.org/10.1080/09243046.2013.871172
  84. A. Ropalekar, R. Ghadge, and N. Anekar, “Experimental investigation on flexural fatigue strength of graphene oxide modified E-Glass epoxy composite beam,” Materials Physics and Mechanics, vol. 52, no. 1, pp. 132-141, 2024.
  85. H. Ma, X. Bai, Y. Ran, X. Wei, and Z. An, “Modeling the Effect of Stress Ratio, Loading Frequency and Fiber Orientation on the Fatigue Response of Composite Materials,” Polymers, vol. 14, no. 14, p. 2772, 2022. https://doi.org/10.3390/polym14142772
  86. W. Ferdous et al., “Testing and modelling the fatigue behaviour of GFRP composites–Effect of stress level, stress concentration and frequency,” Engineering Science and Technology, an International Journal, vol. 23, no. 5, pp. 1223-1232, 2020.
  87. L. R. Xu and V. Bhamidipati, “An Efficient Method to Estimate the S–N Curves of Engineering Materials,” SEM Annu. Conf. Expo. Exp. Mech, no. 2, pp. 2-5, 2002.
  88. H. S. Kim and S. Huang, “SN curve characterisation for composite materials and prediction of remaining fatigue life using damage function,” Journal of Composites Science, vol. 5, no. 3, p. 76, 2021. https://doi.org/10.3390/jcs5030076
  89. L. S. Sigl, P. Mataga, B. Dalgleish, R. McMeeking, and A. Evans, “On the toughness of brittle materials reinforced with a ductile phase,” Acta Metallurgica, vol. 36, no. 4, pp. 945-953, 1988. https://doi.org/10.1016/0001-6160(88)90149-6
  90. N. Eleftheroglou, D. Zarouchas, T. Loutas, R. C. Alderliesten, and R. Benedictus, “Online remaining fatigue life prognosis for composite materials based on strain data and stochastic modeling,” Key Engineering Materials, vol. 713, pp. 34-37, 2016.
  91. K. Kolasangiani, D. Oguamanam, and H. Bougherara, “Straincontrolled fatigue life prediction of Flax-epoxy laminates using a progressive fatigue damage model,” Composite Structures, vol. 266, p. 113797, 2021.
  92. I. N. Yadav and K. B. Thapa, “Strain-based theoretical fatigue damage model of woven glass-epoxy fabric composite material,” Composites Part C: Open Access, vol. 3, p. 100067, 2020.
  93. G. R. Halford, Fatigue and durability of structural materials. Asm International, 2006.
  94. Q. Sun, H.-N Dui, and X.-L. Fan, “A statistically consistent fatigue damage model based on Miner’s rule,” International Journal of Fatigue, vol. 69, pp. 16-21, 2014.
  95. W. Zhongguang, “Fatigue of structures and materials,” ed: National Industrial Press, Beijing, 1999.
  96. H. S. Chen and S. F. Hwang, “A fatigue damage model for composite materials,” Polymer composites, vol. 30, no. 3, pp. 301-308, 2009. https://doi.org/10.1002/pc.20556
  97. H. Mao and S. Mahadevan, “Fatigue damage modelling of composite materials,” Composite structures, vol. 58, no. 4, pp. 405-410, 2002. https://doi.org/10.1016/S0263-8223(02)00126-5
  98. J. A. Epaarachchi, “A study on estimation of damage accumulation of glass fibre reinforce plastic (GFRP) composites under a block loading situation,” Composite Structures, vol. 75, no. 1-4, pp. 88-92, 2006.
  99. B. Liao et al., “Damage accumulation mechanism of composite laminates subjected to repeated low velocity impacts,” International Journal of Mechanical Sciences, vol. 182, p. 105783, 2020. https://doi.org/10.1016/j.ijmecsci.2020.105783
  100. S. Hassanifard and M. Feyzi, “Experimental and numerical investigation of fatigue damage accumulation in composite laminates,” International Journal of Damage Mechanics, vol. 26, no. 6, pp. 840-858, 2017.
  101. M. Kharrat, V. Placet, E. Ramasso, and M. Boubakar, “Influence of damage accumulation under fatigue loading on the AE-based health assessment of composite materials: Wave distortion and AE-features evolution as a function of damage level,” Composites Part A: Applied Science and Manufacturing, vol. 109, pp. 615-627, 2018.
  102. N. D. Batsoulas and G. I. Giannopoulos, “Cumulative Fatigue Damage of Composite Laminates: Engineering Rule and Life Prediction Aspect,” Materials, vol. 16, no. 8, p. 3271, 2023.
  103. A. P. Vassilopoulos, “Fatigue life prediction of composites and composite structures,” 2019.
  104. W. Van Paepegem and J. Degrieck, “A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites,” International Journal of Fatigue, vol. 24, no. 7, pp. 747-762, 2002. https://doi.org/10.1016/S0142-1123(01)00194-3
  105. J.-S. Kim, K.-D. Bae, C. Lee, Y.-J. Kim, W.-S. Kim, and I.-J. Kim, “Fatigue life evaluation of composite material sleeve using a residual stiffness model,” International Journal of Fatigue, vol. 101, pp. 86-95, 2017.
  106. W.-F. Wu, L. Lee, and S. Choi, “A study of fatigue damage and fatigue life of composite laminates,” Journal of Composite Materials, vol. 30, no. 1, pp. 123-137, 1996.
  107. I. N. Yadav and K. B. Thapa, “Fatigue damage model of woven glass-epoxy fabric composite materials,” Journal of Materials Research and Technology, vol. 9, no. 1, pp. 301-306, 2020.
  108. Z. Khan, F. Al-Sulaiman, J. Farooqi, and M. Younas, “Fatigue life predictions in woven carbon fabric/polyester composites based on modulus degradation,” Journal of reinforced plastics and composites, vol. 20, no. 5, pp. 377-398, 2001.
  109. A. T. Beyene and G. Belingardi, “Bending fatigue failure mechanisms of twill fabric E-Glass/Epoxy composite,” Composite Structures, vol. 122, pp. 250-259, 2015.
  110. Y. Zhao, M. Noori, W. A. Altabey, R. Ghiasi, and Z. Wu, “A fatigue damage model for FRP composite laminate systems based on stiffness reduction,” Struct Durab Health Monit, vol. 13, no. 1, pp. 85-103, 2019. https://doi.org/10.32604/sdhm.2019.04695
  111. L. Herrmann, L. P. Mikkelsen, B. N. Legarth, F. Duddeck, and C. F. Niordson, “An efficient stiffness degradation model for layered composites with arbitrarily oriented tunneling and delamination cracks,” Composites Science and Technology, vol. 230, p. 109729, 2022.
  112. H. Liu, Z. Zhang, H. Jia, Y. Liu, and J. Leng, “A modified composite fatigue damage model considering stiffness evolution for wind turbine blades,” Composite Structures, vol. 233, p. 111736, 2020. https://doi.org/10.1016/j.compstruct.2019.111736
  113. P. A. Carraro and M. Quaresimin, “Fatigue damage and stiffness evolution in composite laminates: a damage-based framework,” Procedia engineering, vol. 213, pp. 17-24, 2018.
  114. M. Drvoderic, M. Pletz, and C. Schuecker, “Modeling Stiffness Degradation of Fiber-Reinforced Polymers Based on Crack Densities Observed in Off-Axis Plies,” Journal of composites science, vol. 6, no. 1, p. 10, 2022.
  115. A. D'Amore and L. Grassia, “A method to predict the fatigue life and the residual strength of composite materials subjected to variable amplitude (VA) loadings,” Composite Structures, vol. 228, p. 111338, 2019.
  116. H. Whitworth, “Evaluation of the residual strength degradation in composite laminates under fatigue loading,” Composite structures, vol. 48, no. 4, pp. 261-264, 2000.
  117. A. D’Amore, M. Giorgio, and L. Grassia, “Modeling the residual strength of carbon fiber reinforced composites subjected to cyclic loading,” International Journal of Fatigue, vol. 78, pp. 31-37, 2015. https://doi.org/10.1016/j.ijfatigue.2015.03.012
  118. A. D’Amore and L. Grassia, “Comparative study of phenomenological residual strength models for composite materials subjected to fatigue: Predictions at Constant Amplitude (CA) loading,” Materials, vol. 12, no. 20, p. 3398, 2019.
  119. E. G. Koricho, G. Belingardi, and A. T. Beyene, “Bending fatigue behavior of twill fabric E-glass/epoxy composite,” Composite Structures, vol. 111, pp. 169-178, 2014.
  120. S. Shiri, M. Yazdani, and M. Pourgol-Mohammad, “A fatigue damage accumulation model based on stiffness degradation of composite materials,” Materials & Design, vol. 88, pp. 12901295, 2015. https://doi.org/10.1016/j.matdes.2015.09.114
  121. Z. Wu, G. Fang, M. Fu, X. Chen, J. Liang, and D. Lv, “Random fatigue damage accumulation analysis of composite thin-wall structures based on residual stiffness method,” Composite structures, vol. 211, pp. 546-556, 2019.
  122. A. I. Khan, S. Venkataraman, and I. Miller, “Predicting fatigue damage of composites using strength degradation and cumulative damage model,” Journal of Composites Science, vol. 2, no. 1, p. 9, 2018. https://doi.org/10.3390/jcs2010009
  123. P. Suwarta, M. Fotouhi, G. Czél, M. Longana, and M. R. Wisnom, “Fatigue behaviour of pseudo-ductile unidirectional thin-ply carbon/epoxy-glass/epoxy hybrid composites,” Composite Structures, vol. 224, p. 110996, 2019.
  124. P. C. Paris, “A brief history of the crack tip stress intensity factor and its application,” Meccanica, vol. 49, pp. 759-764, 2014. https://doi.org/10.1007/s11012-014-9896-y
  125. J. D. Rodriguez, “Linear elastic fracture mechanics analysis of fatigue crack growth under complex loading using the Digital Image Correlation technique,” Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil, 2018.
  126. A. O. Mashjel, R. M. Laftah, and H. I. Khalaf, “Study the effect of perforation type for plate with central crack on the stress intensity factor using the XFEM,” Basrah Journal for Engineering Sciences, vol. 21, no. 1, pp. 27-37, 2021.
  127. M. S. Kahyoosh, R. M. Laftah, and A. A. Nassar, “Effect of Fiber Orientation Angle on Stress Intensity Factor of Composite Plate Using Extended Finite Element Method (XFEM),” Basrah Journal for Engineering Sciences, vol. 22, no. 1, pp. 58-68, 2022.
  128. Z. N. Jassam and R. M. Laftah, “Investigation of Stress Intensity Factor Reduction using Steel and GFRP Patches for Repairing Edge Cracks in Steel Plates,” Basrah Journal for Engineering Sciences, vol. 24, no. 1, 2024.
  129. P. G. Nittur, A. M. Karlsson, and L. A. Carlsson, “Numerical evaluation of Paris-regime crack growth rate based on plastically dissipated energy,” Engineering Fracture Mechanics, vol. 124, pp. 155-166, 2014.
  130. D. Atodaria, S. Putatunda, and P. Mallick, “A fatigue crack growth model for random fiber composites,” Journal of Composite Materials, vol. 31, no. 18, pp. 1838-1855, 1997.
  131. R. S. Gupta, H. Xin, and M. Veljkovic, “Fatigue crack propagation simulation of orthotropic bridge deck based on extended finite element method,” Procedia Structural Integrity, vol. 22, pp. 283-290, 2019.
  132. T. Santos, “Numerical study of fatigue cracks propagation in a high strength steel,” Instituto Superior Técnico, Universidade de Lisboa, 2017.
  133. A. Mujtaba, S. Stelzer, A. Brunner, and R. Jones, “Influence of cyclic stress intensity threshold on the scatter seen in cyclic Mode I fatigue delamination growth in DCB tests,” Composite structures, vol. 169, pp. 138-143, 2017.
  134. G. Pitarresi, T. Scalici, M. Dellaira, and G. Catalanotti, “A methodology for the rapid characterization of Mode II delamination fatigue threshold in FRP composites,” Engineering Fracture Mechanics, vol. 220, p. 106629, 2019.
  135. J. Zhang, L. Peng, L. Zhao, and B. Fei, “Fatigue delamination growth rates and thresholds of composite laminates under mixed mode loading,” International Journal of Fatigue, vol. 40, pp. 715, 2012. https://doi.org/10.1016/j.ijfatigue.2012.01.008
  136. S. Bhattacharya, I. Singh, B. Mishra, and T. Bui, “Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM,” Computational Mechanics, vol. 52, pp. 799-814, 2013.
  137. S. Bhattacharya, K. Sharma, and V. Sonkar, “Fatigue fracture of functionally graded materials under elastic-plastic loading conditions using extended finite element method,” Contact and Fracture Mechanics: IntechOpen, 2018.
  138. S. G. Shastry and C. Chandrashekara, “Computational Fatigue Life Analysis of Carbon Fiber Laminate,” IOP Conference Series: Materials Science and Engineering, vol. 310, no. 1, 2018.
  139. M. Arhant, E. Lolive, T. Bonnemains, and P. Davies, “Fatigue crack growth properties of carbon-polyamide 6 thermoplastic composites using a multi-ΔG control method,” Engineering Fracture Mechanics, vol. 252, p. 107825, 2021.
  140. J. Karger-Kocsis, K. Friedrich, and R. Bailey, “Fatigue and failure behavior of short and long glass fiber reinforced injectionmolded polypropylene,” Science and engineering of Composite Materials, vol. 2, no. 1, pp. 49-68, 1991.
  141. M. M. Kadhim and F. A. Alshamma, “Glass laminate aluminum reinforced epoxy under non-proportional multiaxial fatigue loading: Experimental testing and new fatigue apparatus development,” Results in Engineering, vol. 16, p. 100773, 2022.
  142. D. Atodaria, S. Putatunda, and P. Mallick, “Fatigue crack growth model and mechanism of a random fiber SMC composite,” Polymer composites, vol. 20, no. 2, pp. 240-249, 1999. https://doi.org/10.1002/pc.10351
  143. J. S. AbdulRazaq, A. K. F. Hassan, and N. H. J. Al Hasan, “Epoxy–Silica Functionally Graded Materials: A Review,”
  144. O. Attia, A. Kinloch, and F. Matthews, “Modelling the fatigue life of polymer–matrix fibre-composite components,” Composites science and technology, vol. 61, no. 15, pp. 22732283, 2001. https://doi.org/10.1016/S0266-3538(01)00121-X
  145. L. Peng, J. Zhang, L. Zhao, R. Bao, H. Yang, and B. Fei, “Mode I delamination growth of multidirectional composite laminates under fatigue loading,” Journal of composite materials, vol. 45, no. 10, pp. 1077-1090, 2011. https://doi.org/10.1177/0021998310385029
  146. L. Peng, J. Xu, J. Zhang, and L. Zhao, “Mixed mode delamination growth of multidirectional composite laminates under fatigue loading,” Engineering Fracture Mechanics, vol. 96, pp. 676-686, 2012.
  147. M. Y. Shiino, R. C. Alderliesten, M. Y. Pitanga, and M. O. H. Cioffi, “Fatigue crack growth rate in mode i of a carbon fiber 5HS weave composite laminate processed via RTM,” Advanced Materials Research, vol. 891, pp. 172-177, 2014.
  148. J. Wilk, “Compliance based method for testing fatigue delamination propagation in laminates,” Engineering Fracture Mechanics, vol. 203, pp. 137-151, 2018.
  149. O. Al-Khudairi, H. Hadavinia, A. Waggott, E. Lewis, and C. Little, “Characterising mode I/mode II fatigue delamination growth in unidirectional fibre reinforced polymer laminates,” Materials & Design (1980-2015), vol. 66, pp. 93-102, 2015.
  150. S. Rubiera, A. Argüelles, J. Viña, and C. Rocandio, “Study of the phenomenon of fatigue delamination in a carbon-epoxy composite under mixed mode I/II fracture employing an asymmetric specimen,” International Journal of Fatigue, vol. 114, pp. 74-80, 2018. https://doi.org/10.1016/j.ijfatigue.2018.05.015
  151. L. Yao et al., “A modified Paris relation for fatigue delamination with fibre bridging in composite laminates,” Composite Structures, vol. 176, pp. 556-564, 2017.
  152. L. Yao, R. Alderliesten, M. Zhao, and R. Benedictus, “Bridging effect on mode I fatigue delamination behavior in composite laminates,” Composites Part A: Applied Science and Manufacturing, vol. 63, pp. 103-109, 2014.
  153. L. Banks‐Sills and H. B. Gur, “The effect of fiber bridging on mode I fatigue delamination propagation-part I: Testing,” Fatigue & Fracture of Engineering Materials & Structures, 2024.
  154. R. Alderliesten, “Fatigue delamination of composite materials– approach to exclude large scale fibre bridging,” IOP Conference Series: Materials Science and Engineering, vol. 388, no. 1, 2018.
  155. F. M. Monticeli, H. J. Voorwald, and M. O. H. Cioffi, “The influence of carbon-glass/epoxy hybrid composite under mode I fatigue loading: Hybrid fiber bridging zone model,” Composite Structures, vol. 286, p. 115274, 2022.
  156. L. Yao et al., “Fibre-bridged fatigue delamination in multidirectional composite laminates,” Composites Part A: Applied Science and Manufacturing, vol. 115, pp. 175-186, 2018.
  157. A. Darbandi and A. Mirzaei, “Quasi-static cyclic loading assessment of GFRP single-lap adhesive joints reinforced with zpins,” Thin-Walled Structures, vol. 182, p. 110247, 2023.
  158. K. Pingkarawat and A. Mouritz, “Improving the mode I delamination fatigue resistance of composites using z-pins,” Composites science and technology, vol. 92, pp. 70-76, 2014.
  159. B. Gong et al., “Fatigue life assessment and damage evolution in Z-pinned laminates,” Composites Science and Technology, vol. 221, p. 109328, 2022.
  160. F. Warzok, G. Allegri, M. Gude, and S. Hallett, “Experimental study of Z-pin fatigue; understanding of mode I and II coupon behaviour,” Composites Part A: Applied Science and Manufacturing, vol. 127, p. 105615, 2019.
  161. S. Tang, S. Lemanski, X. Zhang, and D. Ayre, “Fatigue life prediction of z-fibre pinned composite laminate under mode I loading,” Composites Science and Technology, vol. 174, pp. 221231, 2019. https://doi.org/10.1016/j.compscitech.2019.02.010
  162. M. Zhu et al., “Digital image correlation assisted