A SEMI-EMPIRICAL MODEL FOR PREDICTING FLEXURAL STRENGTH OF CNT-REINFORCED CFRP BASED ON TENSILE STRENGTH AND INTERFACIAL CONTRIBUTIONS
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Keywords:
Leat-Square Regression, Semi-Empirical Modeling, CFRP, CNTs, Flexural Strength PredictionAbstract
A semi-empirical model is proposed to predict the flexural strength of CNT-reinforced CFRP composites using tensile strength and CNT concentration as primary inputs. The model incorporates three physically meaningful terms, proportional to , to capture matrix toughening, direct CNT reinforcement, and interfacial efficiency. Model parameters were determined via least-squares regression using experimental data from composites with CNT concentrations up to 0.4 wt%. Validation against independent data (0.5–0.8 wt%) showed strong agreement, with errors consistently below 4%. In addition, the model reflects key trends observed in practice: an increase in tensile strength of approximately 20–25% and in flexural strength of about 30–35% at 0.8 wt% CNTs, relative to the baseline. This formulation offers a balanced compromise between physical realism and predictive simplicity, making it useful for materials selection and mechanical design. Future work will extend the model beyond the saturation point to account for CNT agglomeration, nonlinear interfacial behavior, and morphological effects that emerge at higher loadings
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1. Halvaeyfar M. R., Gorji Azandariani M., Zeighami E., Mirhosseini S. M. - Retrofitting fiber-reinforced concrete beams with nano-graphene oxide and CFRP sheet: an experimental study, Arch. Civ. Mech. Eng. 25 (1) (2025) 1-21. https://doi.org/10.1007/s43452-024-01093-3
2. Anish V., Logeshwari J. - A review on ultra high-performance fibre-reinforced concrete with nanomaterials and its applications, J. Eng. Appl. Sci. 71 (1) (2024) 25. https://doi.org/10.1186/s44147-
023-00357-8
3. Raja T., Devarajan Y. - Development of hemp fiber-reinforced epoxy composite with cobalt oxide nanoparticles for fuel cell and energy storage applications, Results Eng. 25 (2025) 103839. https://doi.org/10.1016/j.rineng.2024.103839
4. Musa A. A., Bello A., Adams S. M., Onwualu A. P., Anye V. C., Bello K. A., Obianyo I. I. - Nano-Enhanced Polymer Composite Materials: A Review of Current Advancements and Challenges, Polymers 17 (7) (2025) 893. https://doi.org/10.3390/polym17070893
5. Aikins S. A., Yeboah F. A. B., Enyejo L. A., Kareem L. A. - The Role of Thermomechanical and Aeroelastic Optimization in FRP-Strengthened Structural Elements for High-Performance Aerospace and Civil Applications, Int. J. Sci. Res. Mech. Mater. Eng. 9 (1) (2025) 35-65. https://doi.org/10.32628/IJSRMME25144
6. Rashid A. B., Haque M., Islam S. M., Labib K. R. U. - Nanotechnology-enhanced fiber-reinforced polymer composites: Recent advancements on processing techniques and applications, Heliyon 10 (2) (2024). https://doi.org/10.1016/j.heliyon.2024.e24692
7. Dejene B. K. - Advancing natural fiber-reinforced composites through incorporating ZnO nanofillers in the polymeric matrix: a review, J. Nat. Fibers 21 (1) (2024) 2356015. https://doi.org/10.1080/15440478.2024.2356015
8. Dejene B. K. - Exploring the potential of ZnO nanoparticle-treated fibers in advancing natural fiber reinforced composites: a review, J. Nat. Fibers 21 (1) (2024) 2311304. https://doi.org/10.1080/15440478.2024.2311304
9. Salman A., Hassan A., Ahmed H. I. - Effects of steel fibers and carbon nanotubes on the flexural behavior of hybrid GFRP/steel reinforced concrete beams, Beni-Suef Univ. J. Basic Appl. Sci. 13 (1) (2024) 1-18. https://doi.org/10.1186/s43088-024-00584-9
10. Srinivasa Perumal K. P., Selvarajan L., Mathan Kumar P., Shriguppikar S. - Enhancing mechanical and morphological properties of glass fiber reinforced epoxy polymer composites through rutile nanoparticle incorporation, Prog. Addit. Manuf. 10 (1) (2025) 831-848. https://doi.org/10.1007/s40964-024-00675-0
11. Demircan O., Ibrahim M. H. I., Xiao Z. X., Yang J., Li Q., Wang Z. B., Liu Z. Y., Xiao B. L., Zheng Y. G. - Effect of heat treatment on microstructure, mechanical property and corrosion resistance of a novel Na2MoO4@ CNT/2024 composite, J. Alloys Compd. 1021 (2025) 179607. https://doi.org/10.1016/j.jallcom.2025.179607
12. Imran M., Amjad H., Khan S., Ali S. - Machine learning assisted prediction of the mechanical properties of carbon nanotube‐incorporated concrete, Struct. Concr. 26 (2) (2025) 1613-1635. https://doi.org/10.1002/suco.202400727
13. Karimi S. - Investigating the durability of nano‐reinforced CFRP‐aluminum and CFRP‐CFRP bonded and bonded/bolted joints under hygrothermal conditions, Polym. Compos. 46 (5) (2025) 4075-4095. https://doi.org/10.1002/pc.29225
14. Electric field-assisted alignment of carbon nanotubes in the interlayers of CFRP composites to enhance the properties, Compos. Part A Appl. Sci. Manuf. 190 (2025) 108706. https://doi.org/10.1016/j.compositesa.2024.108706
15. Xing F., He Z., Wang S., Gu Y., Han J., Wang Y., Li M. - Nano‐particles doped carbon nanotube films for in‐situ monitoring of temperature and strain during the processing of carbon fiber/epoxy composites, Polym. Compos. 46 (1) (2025) 193-207. https://doi.org/10.1002/pc.28978
16. Nurguzhin M., Janikeyev M., Omarbayev M., Yermakhanova A., Meiirbekov M., Zhumakhanov M., Yerezhep D. - Structure and Properties of Al–CNT-Based Composites Manufactured by Different Methods: A Brief Review, Materials 18 (1) (2025) 214. https://doi.org/10.3390/ma18010214
17. Weng Y., Wu L., Ou Y., Mao D. - Short carbon nanotubes: from matrix toughening to interlaminar toughening of CFRP composites, Compos. Commun. 41 (2023) 101652. https://doi.org/10.1016/j.coco.2023.101652
18. Kavitha S. S., Joseph L., Kumar P. S., Sarker P. K., Madhavan M. K., Jayanarayanan K. - Implementation of multi-walled carbon nanotube incorporated GFRP as an alternative for CFRP in strengthening of concrete cylinders, Struct. 70 (2024) 107606. Elsevier. https://doi.org/10.1016/j.istruc.2024.107606
19. Ghosh P., Ramajeyathilagam K. - Experimental and numerical investigation on Multiwalled carbon nanotubes (MWCNTs) dispersed CFRP laminate subjected to spherical and conical impacts, Ships Offshore Struct. 19 (12) (2024) 2024-2039. https://doi.org/10.1080/17445302.2024.2317660
20. Liu J., Yang T., Wang B., Yu Z., Yang Y., Sun G. - Mechanical improvement of carbon fiber/epoxy composites by sizing functionalized carbon nanotubes on fibers, Polym. Compos. 45 (12) (2024) 10645-10653. https://doi.org/10.1002/pc.28497
21. Xu L. Y., Wang X. Y., Lin Y. Z., Huang Y., Tao C. C., Zhang D. W. - Experimental and numerical investigations of carbon-based nanoparticle reinforcement on microstructure and mechanical properties of epoxy coatings, Chin. J. Polym. Sci. 43 (1) (2025) 211-224. https://doi.org/10.1007/s10118-025-3252-7
22. Rahimijonoush A., Mohammadimehr M. - The effect of nanoparticles on cold roll bonded fiber metal laminates under high-velocity impact: experimental and numerical approaches, J. Braz. Soc. Mech. Sci. Eng. 47 (4) (2025) 183. https://doi.org/10.1007/s40430-025-05486-0
23. Li Y., Li H., Song C., Zhu Z., Ma X. - Molecular dynamics simulations of the micro mechanism of functionalized SiO2 nanoparticles and carbon nanotubes modified epoxy resin adhesives, Polym. Compos. 46 (2) (2025) 1587-1603. https://doi.org/10.1002/pc.29059
24. Cao M., Wang S., Zang J., Liu M., Qian C., Zhang Y., Na D. - Experimental and simulation analysis of the effect of GNPs on the mechanical and interfacial properties of CF/PEEK-Ti fiber metal laminates, Compos. Sci. Technol. 246 (2024) 110387. https://doi.org/10.1016/j.compscitech.2023.110387
25. Li Y., Li H., Song C., Zhu Z., Ma X. - Molecular dynamics simulations of the micro mechanism of functionalized SiO2 nanoparticles and carbon nanotubes modified epoxy resin adhesives, Polym. Compos. 46 (2) (2025) 1587-1603. https://doi.org/10.1002/pc.29059
26. Zhang M., Yu Y., Luan Y., Zhou H., Peng X., Gong L., Zhou H. - Effects of CNT microstructural characteristics on the interfacial enhancement mechanism of carbon fiber reinforced epoxy composites via molecular dynamics simulations, Thin-Walled Struct. 195 (2024) 111413. https://doi.org/10.1016/j.tws.2023.111413
27. Ascione F., De Maio U., Greco F., Lonetti P., Sgambitterra G., Pranno A. - Failure analysis of RC structures retrofitted with nano-enhanced FRP systems, Procedia Struct. Integr. 47 (2023) 460-468. https://doi.org/10.1016/j.prostr.2023.07.078
28. Chang W., Rose L. F., Sha Z., Huang F., Kinloch A. J., Wang C. H. - Multiscale modelling of nanoparticle toughening in epoxy: Effects of particle-matrix interface, particle size, and volume fraction, Compos. Sci. Technol. 256 (2024) 110788. https://doi.org/10.1016/j.compscitech.2024.110788
29. Ghosh P., Ramajeyathilagam K. - Experimental and numerical investigations on the effect of MWCNT-COOH and Al2O3 hybrid nanofillers dispersed CFRP laminates subjected to projectile impact, Processes 11 (5) (2023) 1435. https://doi.org/10.3390/pr11051435
30. Shaki M. H., Rostamiyan Y., Seyyedi S. M. - Three-point bending performance of circular-shaped core foam-filled sandwich panels reinforced with carbon fibers and silica nanoparticles, Funct. Compos. Struct. 7 (2) (2025) 025001. https://doi.org/10.1088/2631-6331/adc9f9
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Vietnam Academy of Science and Technology
Grant numbers CSCL39.01/25-26
