Fracture Behavior of a Unidirectional Carbon Fiber-Reinforced Plastic under Biaxial Tensile Loads
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Preparation Method of Cruciform Specimen
2.3. Stress Distribution
2.4. Biaxial Tensile Test
3. Results and Discussion
3.1. Fracture Modes
3.2. Strain Histories and Fracture Strains
4. Conclusions
- (1)
- Biaxial tensile fracture of the unidirectional CFRP is enabled by a cruciform specimen with a gauge area longer in the fiber direction than in the fiber vertical direction at the center. This is applicable regardless of proportional or non-proportional loading.
- (2)
- There were three fracture modes in the specimens: a transverse crack (TC), fiber breakage (FB), and both modes (TC&FB) occurring simultaneously. The TC&FB mode is a unique mode that does not appear in the fracture modes under uniaxial tension (FB and TC), but only under biaxial tensile loading.
- (3)
- Under several conditions of proportional loading, the failure loads in the 0° direction, indicating the FB and TC&FB modes, were almost identical. In another condition, the fracture loads in the 90° direction, indicating the TC and TC&FB modes, were close to each other. From the aspect of fractured specimens, it was finally inferred that the TC occurred before FB, and the occurrence of the TC triggered FB instantaneously.
- (4)
- The TC and TC&FB modes occurred when the strain in the 90° direction, , was positive. On the other hand, the FB mode occurred when was negative despite the fact that FB and TC&FB modes showed almost the same strains in the 0° direction. It was concluded that the occurrence of each fracture mode is characterized by only one parameter, namely .
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Kaddour, A.S.; Hinton, M.J.; Soden, P.D. A comparison of the predictive capabilities of current failure theories for composite laminates: Additional contributions. Compos. Sci. Technol. 2004, 64, 449–476. [Google Scholar] [CrossRef]
- Hinton, M.J.; Kaddour, A.S.; Soden, P.D. A further assessment of the predictive capabilities of current failure theories for composite laminates comparison with experimental evidence. Compos. Sci. Technol. 2004, 64, 549–588. [Google Scholar] [CrossRef]
- Christensen, R.M. Failure criteria for fiber composite materials, the astonishing sixty year search, definitive usable results. Compos. Sci. Technol. 2019, 182, 107718. [Google Scholar] [CrossRef]
- Daniel, I.M. Yield and failure criteria for composite materials under static and dynamic loading. Prog. Aerosp. Sci. 2016, 81, 18–25. [Google Scholar] [CrossRef]
- Kaddour, A.S.; Hinton, M.J.; Smith, P.A.; Li, S. A comparison between the predictive capability of matrix cracking, damage and failure criteria for fibre reinforced composite laminates: Part A of the third world-wide failure exercise. J. Compos. Mater. 2013, 47, 2749–2779. [Google Scholar] [CrossRef]
- Puck, A.; Schürmann, H. Failure analysis of FRP laminates by means of physically based phenomenological models. Compos. Sci. Technol. 2002, 62, 1633–1662. [Google Scholar] [CrossRef]
- Pinho, S.T.; Iannucci, L.; Robinson, P. Physically based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking. Part II: FE implementation. Compos. Part A 2006, 37, 766–777. [Google Scholar] [CrossRef]
- Clyne, T.W.; Hull, D. Chapter 1: General Introduction. In An Introduction to Composite Materials, 3rd ed.; Cambridge University Press: Cambridge, UK, 2019; pp. 1–8. [Google Scholar]
- Tsai, S.W.; Wu, E.M. A general theory of strength for anisotropic materials. J. Compos. Mater. 1971, 5, 58–80. [Google Scholar] [CrossRef]
- Hashin, Z. Failure Criteria for unidirectional fiber composites. J. Appl. Mech. 1980, 47, 329–334. [Google Scholar] [CrossRef]
- Christensen, R.M. Stress based yield/failure criteria for fiber composites. Int. J. Solids Struct. 1997, 34, 529–543. [Google Scholar] [CrossRef]
- Pinho, S.T.; Iannucci, L.; Robinson, P. Physically-based failure models and criteria for laminated fibre-reinforced composites: Part I: Development. Compos. Part A 2006, 37, 63–73. [Google Scholar] [CrossRef]
- Gu, J.; Chen, P. Some modifications of Hashin’s failure criteria for unidirectional composite materials. Compos. Struct. 2017, 182, 143–152. [Google Scholar] [CrossRef]
- Wan, L.; Ismail, Y.; Sheng, Y.; Ye, J.; Yang, D. A review on micromechanical modelling of progressive failure in unidirectional fibre-reinforced composites. Compos. Part C Open Access 2023, 10, 100348. [Google Scholar] [CrossRef]
- Wan, L.; Ullah, Z.; Yang, D.; Falzon, B.G. Probability embedded failure prediction of unidirectional composites under biaxial loadings combining machine learning and micromechanical modelling. Compos. Struct. 2023, 312, 116837. [Google Scholar] [CrossRef]
- Matzenmiller, A.; Lubliner, J.; Taylor, R.L. A constitutive model for anisotropic damage in fiber-composites. Mech. Mater. 1995, 20, 125–152. [Google Scholar] [CrossRef]
- Maimí, P.; Camanho, P.P.; Mayugo, J.A.; Dávila, C.G. A continuum damage model for composite laminates Part I—Constitutive model. Mech. Mater. 2007, 39, 897–908. [Google Scholar] [CrossRef]
- Liu, P.F.; Zheng, J.Y. Progressive failure analysis of carbon fiber epoxy composite laminates using continuum damage mechanics. Mater. Sci. Eng. A 2008, 485, 711–717. [Google Scholar] [CrossRef]
- Shahabi, E.; Forouzan, M.R. A damage mechanics based failure criterion for fiber reinforced polymers. Compos. Sci. Technol. 2017, 140, 23–29. [Google Scholar] [CrossRef]
- Ismail, Y.; Sheng, Y.; Yang, D.; Ye, J. Discrete element modelling of unidirectional fibre-reinforced polymers, under transverse tension. Compos. Part B 2015, 73, 118–125. [Google Scholar] [CrossRef]
- González, C.; Llorca, J. Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling. Compos. Sci. Technol. 2007, 67, 2795–2806. [Google Scholar] [CrossRef]
- Romanowicz, M. A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension. Comput. Mater. Sci. 2012, 51, 7–12. [Google Scholar] [CrossRef]
- Totry, E.; Molina-Aldareguía, J.M.; González, C.; Llorca, J. Effect of fiber, matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites. Compos. Sci. Technol. 2010, 70, 970–980. [Google Scholar] [CrossRef]
- Tory, E.; González, C.; Llorca, J. Failure locus of fiber-reinforced composites under transverse compression and out-of-plane shear. Compos. Sci. Technol. 2008, 68, 829–839. [Google Scholar] [CrossRef]
- Soden, P.D.; Hinton, M.J.; Kaddour, A.S. Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: Failure exercise benchmark data. Compos. Sci. Technol. 2002, 62, 1489–1514. [Google Scholar] [CrossRef]
- Youssef, Y.; Labonte, S.; Roy, C.; Lefebvre, D. An Effective Flat Cruciform-Shaped Specimen for Biaxial Testing of CFRP laminates. Sci. Eng. Compos. Mater. 1994, 3, 259–267. [Google Scholar] [CrossRef]
- Kumazawa, H.; Hayashi, H.; Susuki, I.; Utsunomiya, T. Damage and permeability evolution in CFRP cross-ply laminates. Compos. Struct. 2006, 76, 73–81. [Google Scholar] [CrossRef]
- Gower, M.R.L.; Shaw, R.M. Towards a Planar Cruciform Specimen for Biaxial Characterisation of Polymer Matrix Composites. Appl. Mech. Mater. 2010, 24–25, 115–120. [Google Scholar]
- Gutiérrez, J.C.; Lozano, A.; Manzano, A.; Flores, M.S. Numerical and Experimental Analysis for Shape Improvement of a Cruciform Composite Laminates Specimen. Fibres Text. East. Eur. 2016, 24, 89–94. [Google Scholar] [CrossRef]
- Zhang, X.; Zhu, H.; Lv, Z.; Zhao, X.; Wang, J.; Wang, Q. Investigation of Biaxial Properties of CFRP with the Novel-Designed Cruciform Specimens. Materials 2022, 15, 7034. [Google Scholar] [CrossRef]
- Correa, E.; Barroso, A.; Pérez, M.D.; París, F. Design for a cruciform coupon used for tensile biaxial transverse tests on composite materials. Compos. Sci. Technol. 2017, 145, 138–148. [Google Scholar] [CrossRef]
- Goto, K.; Arai, M.; Nishimura, M.; Dohi, K. Strength evaluation of unidirectional carbon fiber reinforced plastic laminates based on tension-compression biaxial stress tests. J. Jpn. Soc. Compos. Mater. 2017, 43, 48–57. [Google Scholar] [CrossRef]
- Rev, T.; Wisnom, M.R.; Xu, X.; Czél, G. The effect of transverse compressive stresses on tensile failure of carbon fibre/epoxy composites. Compos. Part A 2022, 156, 106894. [Google Scholar] [CrossRef]
- Potter, D.; Gupta, V.; Chen, X.; Tian, J. Mechanisms-based failure laws for AS4/3502 graphite/epoxy laminates under in-plane biaxial compression. Compos. Sci. Technol. 2005, 65, 2105–2117. [Google Scholar] [CrossRef]
- Kang, H.; Liang, J.; Li, Y.; Cui, H.; Li, Y. Dynamic biaxial compression of CFRP laminates using electromagnetic loading. Acta Mech. Solida Sin. 2022, 35, 891–900. [Google Scholar] [CrossRef]
- Nakasaki, S.; Nakamura, S.; Kataoka, Y.; Macadre, A.; Goda, K. Fracture Characteristics of Unidirectional CFRP Composites under Biaxial Tensile Load. J. Jpn. Soc. Compos. Mater. 2022, 48, 77–85. [Google Scholar] [CrossRef]
- Hart-Smith, L.J. Predictions of the original and truncated maximum-strain failure models for certain fibrous composite laminates. Compos. Sci. Technol. 1998, 58, 1151–1178. [Google Scholar] [CrossRef]
- MITSUBISHI CHEMICAL Corp. Available online: https://www.m-chemical.co.jp/carbon-fiber/en/product/tow/ (accessed on 10 February 2024).
- Fineberg, J.; Marder, M. Instability in dynamic fractur. Phys. Rep. 1999, 313, 1–108. [Google Scholar] [CrossRef]
- Lee, J.; Hong, J.W. Dynamic crack branching and curving in brittle polymers. Int. J. Solids Struct. 2016, 100–101, 332–340. [Google Scholar] [CrossRef]
- Hull, D. Chapter 5: Elastic properties. In An Introduction to Composite Materials, 1st ed.; Cambridge University Press: Cambridge, UK, 1981; pp. 81–101. [Google Scholar]
- Clyne, T.W.; Hull, D. Chapter 3: Elastic Deformation of Long Fiber Composites. In An Introduction to Composite Materials, 3rd ed.; Cambridge University Press: Cambridge, UK, 2019; pp. 31–42. [Google Scholar]
Constituent Material | Density [Mg/m3] | Filament Diameter [mm] | Tensile Strength [MPa] | Young’s Modulus [GPa] | Fracture Strain [%] | [MPa] | [MPa] |
---|---|---|---|---|---|---|---|
CF tow | 1.82 | 7 | 4900 | 235 | - | - | - |
Epoxy resin | 1.16 | - | 65.2 | 3.2 | 5.0 | 48.0 | 447 |
E1 = 112.8 [GPa] | ν12 = 0.38 | G12 = 6.0 [GPa] |
E2 = 6.6 [GPa] | ν13 = 0.38 | G13 = 6.0 [GPa] |
E3 = 6.6 [GPa] | ν23 = 0.49 | G23 = 2.2 [GPa] |
Applied Loads | Simulated Stresses | ||
---|---|---|---|
[N] | [N] | [MPa] | [MPa] |
50 | 100 | 3.7–6.8 | 6.6–10.4 |
100 | 100 | 17.7–20.5 | 6.6–10.1 |
200 | 100 | 45.5–48.1 | 6.6–9.6 |
400 | 100 | 101–103 | 6.4–8.5 |
800 | 100 | 210–212 | 6.1–6.6 |
1000 | 100 | 267–279 | 5.2–6.2 |
1400 | 100 | 377–380 | 3.5–5.8 |
1000 | - | 285–286 | 0.06–0.52 |
Loading Condition | Cross-Head Speed | Cross-Head Speed Ratio | |
---|---|---|---|
x-Axis [mm/s] | y-Axis [mm/s] | ||
B11 | 0.01 | 0.01 | 1:1 |
B21 | 0.02 | 0.01 | 2:1 |
B31 | 0.03 | 0.01 | 3:1 |
B41 | 0.04 | 0.01 | 4:1 |
B51 | 0.05 | 0.01 | 5:1 |
B12 | 0.01 | 0.02 | 1:2 |
B114 | 0.01 | 0.14 | 1:14 |
U10 | 0.01 | - | - |
Loading Condition | Number of Specimens | Fracture Loads [N] | Fracture Mode | |
---|---|---|---|---|
B11 | 3 | 3292 | 835 | TC |
B21 | 3 | 5728 | 818 | TC&FB |
B31 | 3 | 7457 | 773 | TC&FB |
B41 | 3 | 7415 | 595 | FB * |
B51 | 3 | 8058 | 567 | FB |
B12 | 3 | 1608 | 825 | TC |
B114 | 3 | 235 | 685 | TC |
U10 | 3 | 7318 | 0 | FB |
Loading Condition | Number of Specimens | Fixed Load [N] | Fracture Load [N] | Fracture Mode | ||
---|---|---|---|---|---|---|
X2Y1 * | 3 | - | 460 | 7203 | - | FB |
X2Y1 | 1 | - | 610 | 6605 | FB | |
X2Y1 | 1 | - | 420 | 6535 | FB | |
X1Y2 | 1 | 5515 | - | 890 | TC&FB | |
X1Y2 | 3 | 4500 | - | 807 | TC&FB | |
X1Y2 | 2 | 2265 | - | 813 | TC | |
X1Y2 | 7 | 2200 | - | - | 853 | TC |
X1Y2 | 2 | 500 | 790 | TC |
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Sanai, K.; Nakasaki, S.; Hashimoto, M.; Macadre, A.; Goda, K. Fracture Behavior of a Unidirectional Carbon Fiber-Reinforced Plastic under Biaxial Tensile Loads. Materials 2024, 17, 1387. https://doi.org/10.3390/ma17061387
Sanai K, Nakasaki S, Hashimoto M, Macadre A, Goda K. Fracture Behavior of a Unidirectional Carbon Fiber-Reinforced Plastic under Biaxial Tensile Loads. Materials. 2024; 17(6):1387. https://doi.org/10.3390/ma17061387
Chicago/Turabian StyleSanai, Kosuke, Sho Nakasaki, Mikiyasu Hashimoto, Arnaud Macadre, and Koichi Goda. 2024. "Fracture Behavior of a Unidirectional Carbon Fiber-Reinforced Plastic under Biaxial Tensile Loads" Materials 17, no. 6: 1387. https://doi.org/10.3390/ma17061387