A Multiscale Modelling Approach for Estimating the Effect of Defects in Unidirectional Carbon Fiber Reinforced Polymer Composites
Abstract
:1. Introduction
2. Materials and Methods
2.1. Constituent Properties
2.2. Microstructure
2.3. Microscale Modelling
2.4. Macroscale Modelling
3. Results
3.1. Constituent Properties
3.2. Microstructure
3.3. Microscale Modelling
3.4. Macroscale Modelling
3.5. Effect of Defects
4. Conclusions
- Fiber and resin properties given by manufacturers should be taken with caution, considering the measurement methodology is not known. Determining constituent properties with nanoindentation gives poor results for both longitudinal fiber and matrix properties. The phenomena could be attributed to nanoscale buckling of the fiber and a constraint effect in the matrix, respectively. Transverse nanoindentation results of the fiber were closer to inverse micromechanics solutions and literature values of similar fibers. Despite the uncertainty in input parameters, the homogenised composite properties were in good agreement with experimental verifications.
- SEM images were successfully segmented algorithmically enabling the generation of a representative mesh of the microstructure. However, the use of 2D micrographs omits fiber waviness effects and defect morphology.
- Macroscale simulations were in good agreement with experimental work both in terms of elastic response and failure location. A sensitivity analysis showed that only the longitudinal modulus of the composite plays a significant role in the macroscale response. Furthermore, that parameter is mainly affected by the longitudinal fiber modulus, which is typically known. In fact, transverse properties are insignificant to a degree where an assumption of isotropic material properties leads only to a 3% error in stress/strain. However, three-point bending was the only load case used.
- A batch of high-porosity material was produced and the effect of porosity was simulated using a resin-rich area in the microstructure. The simulations show stress and strain concentrations in the fibers and matrix due to the heterogeneous microstructure. However, long-beam bending experiments showed no difference in strength between reference and porous samples. This can be attributed to the load sharing mechanism of unidirectional reinforcement fibers in predominantly tensile loading. However, short-beam bending experiments showed a 20% reduction in apparent shear strength for the samples with porosity. The effect of matrix defects on shear strength was simulated by looking at the shear strains in the center plane where failure occurred. The results depict a highly strained matrix at the resin-rich zone compared to a homogeneous microstructure.
Author Contributions
Funding
Conflicts of Interest
References
- Rizzo, P.; di Scalea, L. Acoustic emission monitoring of carbon-fiber-reinforced-polymer bridge stay cables in large-scale testing. Exp. Mech. 2001, 41, 282–290. [Google Scholar] [CrossRef]
- Rebel, G.; Verreet, R.; Ridge, I.M.L. Lightweight ropes for lifting applications. In Proceedings of the OIPEEC Conference, Athens, Greece, 27–29 March 2006; pp. 33–54. [Google Scholar]
- Antin, K.-N.; Machado, M.A.; Santos, T.G.; Vilaça, P. Evaluation of different non-destructive testing methods to detect imperfections in unidirectional carbon fiber composite ropes. J. Nondestruct. Eval. 2019, 38, 23. [Google Scholar] [CrossRef]
- Machado, M.A.; Antin, K.-N.; Rosado, L.S.; Vilaça, P.; Santos, T.G. Contactless high-speed eddy current inspection of unidirectional carbon fiber reinforced polymer. Compos. Part B Eng. 2019, 168, 226–235. [Google Scholar] [CrossRef]
- Hedgepeth, J.M.; van Dyke, P. Local stress concentrations in imperfect filamentary composite materials. J. Compos. Mater. 1967, 1, 294–309. [Google Scholar] [CrossRef]
- Landis, C.M.; McMeeking, R.M. Stress concentrations in composites with interface sliding, matrix stiffness and uneven fiber spacing using shear lag theory. Int. J. Solids Struct. 1999, 36, 4333–4361. [Google Scholar] [CrossRef]
- Otero, J.A.; Rodriguez-Ramos, R.; Bravo-Castillero, J.; Guinovart-Diaz, R.; Sabina, F.J.; Monsivais, G. Semi-analytical method for computing effective properties in elastic composite under imperfect contact. Int. J. Solids Struct. 2013, 50, 609–622. [Google Scholar] [CrossRef] [Green Version]
- Sun, C.T.; Vaidya, R.S. Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 1996, 56, 171–179. [Google Scholar] [CrossRef]
- Mishnaevsky, L., Jr.; Broensted, P. Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: A review. Comput. Mater. Sci. 2009, 44, 1351–1359. [Google Scholar] [CrossRef]
- Wongsto, A.; Li, S. Micromechanical FE analysis of UD fibre-reinforced composites with fibres distributed at random over the transverse cross-section. Compos. Part A 2005, 36, 1246–1266. [Google Scholar] [CrossRef]
- Dong, C. Effects of Process-Induced Voids on the Properties of Fibre Reinforced Composites. J. Mater. Sci. Technol. 2016, 7, 597–604. [Google Scholar] [CrossRef]
- Swolfs, Y.; Gorbatikh, L.; Romanov, V.S.; Orlova, S.; Lomov, S.V.; Verpoest, I. Stress concentrations in an impregnated fibre bundle with random fibre packing. Compos. Sci. Technol. 2013, 74, 113–120. [Google Scholar] [CrossRef]
- Vaughan, T.J.; McCarthy, C.T. Micromechanical modelling of the transverse damage behaviour in fibre reinforced composites. Compos. Sci. Technol. 2011, 71, 388–396. [Google Scholar] [CrossRef]
- Maurin, R.; Davies, P.; Baral, N.; Baley, C. Transverse properties of carbon fibres by nano-indentation and micro-mechanics. Appl. Compos. Mater. 2008, 15, 61–73. [Google Scholar] [CrossRef]
- Beicha, D.; Kanit, T.; Brunet, Y.; Imad, A.; El Moumen, A.; Khelfaoui, Y. Effective transverse elastic properties of unidirectional fiber reinforced composites. Mech. Mater. 2016, 102, 47–53. [Google Scholar] [CrossRef]
- Schumacher, D.; Antin, K.-N.; Zscherpel, U.; Vilaça, P. Application of different X-ray techniques to improve in-service carbon fiber reinforced rope inspection. J. Nondestruct. Eval. 2017, 36, 1–14. [Google Scholar] [CrossRef]
- Halpin, J.C.; Kardos, J.L. The Halpin-Tsai equations: A review. Polym. Eng. Sci. 1976, 16, 344–352. [Google Scholar]
- Sarlin, E.; von Essen, M.; Palola, S.; Lindgren, M.; Kallio, P.; Vuorinen, J. Determination of environmental degradation of matrix and fiber materials with a novel, stastically reliable micro-robotic approach. In Proceedings of the 17th European Conference on Composite Materials ECCM17, München, Germany, 26–30 June 2016. [Google Scholar]
- Ilankeeran, P.K.; Mohite, P.M.; Kamle, S. Axial tensile testing of single fibres. Mod. Mech. Eng. 2012, 2, 151–156. [Google Scholar] [CrossRef]
- Chamis, C.C. Simplified composite micromechanics equations for hygral, thermal and mechanical properties. NASA Technical Memorandum 83320. In Proceedings of the 38th Annual Conference of the Society of the Plastics Industry, Houston, TX, USA, 7–11 February 1983. [Google Scholar]
- Mounier, D.; Poilane, C.; Bucher, C.; Picart, P. Evaluation of transverse elastic properties of fibers used in composite materials by laser resonant ultrasound spectroscopy. In Proceedings of the Acoustics Conference, Nantes, France, 23–27 April 2012. [Google Scholar]
- Soden, P.D.; Hinton, M.J.; Kaddour, A.S. Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates. Compos. Sci. Technol. 1998, 58, 1011–1022. [Google Scholar] [CrossRef]
- Turon, A.; Costa, J.; Maimi, P.; Trias, D.; Mayugo, J.A. A progressive damage model for unidirectional fibre-reinforced composites based on fibre fragmentation. Part I: Formulation. Compos. Sci. Technol. 2005, 65, 2039–2048. [Google Scholar] [CrossRef]
- Blassiau, S.; Thionnet, A.; Bunsell, A.R. Micromechanisms of load transfer in a unidirectional carbon fibre–reinforced epoxy composite due to fibre failures. Part 1: Micromechanisms and 3D analysis of load transfer: The elastic case. Compos. Struct. 2006, 74, 303–318. [Google Scholar] [CrossRef]
- Behzadi, S.; Jones, F.R. The effect of temperature on stress transfer between a broken fibre and the adjacent fibres in unidirectional fibre composites. Compos. Sci. Technol. 2010, 68, 2690–2696. [Google Scholar] [CrossRef]
- Bouaoune, L.; Brunet, Y.; El Moumen, A.; Kanit, T.; Mazouz, H. Random versus periodic microstructures for elasticity of fibers reinforced composites. Compos. Part B 2016, 103, 68–73. [Google Scholar] [CrossRef]
- Melro, A.R.; Camanho, P.P.; Pinho, S.T. Generation of random distribution of fibres in long-fibre reinforced composites. Compos. Sci. Technol. 2008, 68, 2092–2102. [Google Scholar] [CrossRef]
- Swolfs, Y.; Verpoest, I.; Gorbatikh, L. Issues in strength models for unidirectional fibre-reinforced composites related to Weibull distributions, fibre packings and boundary effects. Compos. Sci. Technol. 2015, 114, 42–49. [Google Scholar] [CrossRef] [Green Version]
- Okabe, T.; Takeda, N.; Kamoshida, Y.; Shimizu, M.; Curtin, W.A. A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites. Compos. Sci. Technol. 2001, 61, 1773–1787. [Google Scholar] [CrossRef]
- Trias, D.; Costa, J.; Mayugo, J.A.; Hurtado, J.E. Random models versus periodic models for fibre reinforced composites. Comput. Mater. Sci. 2006, 38, 316–324. [Google Scholar] [CrossRef]
- Holmberg, K.; Laukkanen, A.; Turunen, E.; Laitinen, T. Wear resistance optimisation of composite coatings by computational microstructural modelling. Surf. Coat. Technol. 2014, 247, 1–13. [Google Scholar] [CrossRef]
- Orell, O.; Vuorinen, J.; Jokinen, J.; Kettunen, H.; Hytönen, P.; Turunen, J.; Kanerva, M. Characterization of elastic constants of anisotropic composites in compression using digital image correlation. Compos. Struct. 2018, 185, 176–185. [Google Scholar] [CrossRef]
- Haj-Ali, R.; Kilic, H. Nonlinear constitutive model for pultruded FRP composites. Mech. Mater. 2003, 35, 791–801. [Google Scholar] [CrossRef]
- Fiedler, B.; Holst, S.; Hobbiebrunken, T.; Hojo, M.; Schulte, K. Modelling of the initial failure of CFRP structures by partial discretisation: A micro/macro-mechanical approach of first ply failure. Adv. Compos. Lett. 2004, 13. [Google Scholar] [CrossRef]
- Fliegener, S.; Luke, M.; Gumbsch, P. 3D microstructure modeling of long fiber reinforced thermoplastics. Compos. Sci. Technol. 2014, 104, 136–145. [Google Scholar] [CrossRef]
- Miyagawa, H.; Mase, T.; Sato, C.; Drown, E.; Drzal, L.T.; Ikegami, K. Comparison of experimental and theoretical transverse elastic modulus of carbon fibers. Carbon 2006, 44, 2002–2008. [Google Scholar] [CrossRef]
- Diss, P.; Lamon, J.; Carpentier, L.; Loubet, J.L.; Kapsa, P. Sharp indentation behavior of carbon/carbon composites and varities of carbon. Carbon 2002, 40, 2567–2579. [Google Scholar] [CrossRef]
- Oliver, W.C.; Pharr, G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 1992, 7, 1564–1583. [Google Scholar] [CrossRef]
- Oliver, W.C.; Pharr, G.M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 2004, 19, 3–20. [Google Scholar] [CrossRef]
- Vlassak, J.J.; Ciavarella, M.; Barber, J.R.; Wang, X. The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 2003, 5, 1701–1721. [Google Scholar] [CrossRef]
- Delafargue, A.; Ulm, F.-J. Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters. Inter. J. Solids Struct. 2004, 41, 7351–7360. [Google Scholar] [CrossRef]
- Csanadi, T.; Nemeth, D.; Zhang, C.; Dusza, J. Nanoindentation derived elastic constants of carbon fibres and their nanostructural based predictions. Carbon 2017, 119, 314–325. [Google Scholar] [CrossRef] [Green Version]
- Hashin, Z. Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J. Mech. Phys. Solids 2002, 50, 2509–2537. [Google Scholar] [CrossRef]
- Tang, Z.; Wang, C.; Yu, Y. Failure response of fiber-epoxy unidirectional laminate under transverse tensile/compressive loading using finite-volume micromechanics. Compos. Part B 2015, 79, 331–341. [Google Scholar] [CrossRef]
- Plastics—Determination of tensile properties—Part 5: Test conditions for unidirectional fibre-reinforced plastic composites; ISO 527-5: 2009; International Organization for Standardization: Geneva, Switzerland, 2009.
- Smyl, D.; Antin, K.-N.; Dong, L.; Bossuyt, S. Coupled digital image correlation and quasi-static elasticity imaging of inhomogeneous orthotropic composite structures. Inverse Probl. 2018, 34, 1–26. [Google Scholar] [CrossRef]
- Qiao, Y.; Bisagni, C.; Bai, Y. Experimental investigation and numerical simulation of unidirectional carbon fiber composite under multi-axial loadings. Compos. Part B 2017, 124, 190–206. [Google Scholar] [CrossRef]
- Fibre-reinforced plastic composites—Determination of flexural properties; ISO 14125:1998; International Organization for Standardization: Geneva, Switzerland, 1998.
- Fibre-reinforced plastic composites—Determination of apparent interlaminar shear strength by short-beam method; ISO 14130:1997; International Organization for Standardization: Geneva, Switzerland, 1997.
- Oscan, S.; Tezcan, J.; Filip, P. Microstructure and elastic properties of individual components of C/C composites. Carbon 2009, 47, 3403–3414. [Google Scholar] [CrossRef]
- Marx, D.T.; Riester, L. Mechanical properties of carbon-carbon composite components determined using nanoindentation. Carbon 1999, 37, 1679–1684. [Google Scholar] [CrossRef]
- Leatherbarrow, A.; Wu, H. Mechanical behaviour of the constituents inside carbon-fibre/carbon-silicon carbide composites characterised by nano-indentation. J. Eur. Ceram. Soc. 2012, 32, 579–588. [Google Scholar] [CrossRef] [Green Version]
- Hardiman, M.; Vaughan, T.J.; McCarthy, C.T. The effect of fibre constraint in the nanoindentation of fibrous composite microstructures: A finite element investigation. Comput. Mater. Sci. 2012, 64, 162–167. [Google Scholar] [CrossRef]
Constituent | E1 (GPa) | E2 (GPa) | G12 (GPa) | G23 (GPa) | ν12 | ν23 (Calculated) |
---|---|---|---|---|---|---|
Fiber, f | 239 | 20 | 30 | 8 | 0.2 | 0.25 |
Matrix, m | 3.2 | - | - | - | 0.35 | - |
Location | Contact Stiffness, S (mN/µm) | Indentation Modulus, M (GPa) | Young’s Modulus, E (GPa) | Reference, E (GPa) |
---|---|---|---|---|
Fiber, long. | 46 ± 4 | 50 | 55 | 239 |
Fiber, trans. | 17.5 ± 0.9 | 19 | 13 | 20 |
Matrix | 13 ± 3 | 11 | 13 | 3 |
Property | Multiplier | E1 | E2 | G12 | ν12 | ν23 |
---|---|---|---|---|---|---|
E1f | 0.5 | ↓ 0.5 | - | → 0.8 | - | - |
E1f | 2 | ↑ 2 | - | → 1.2 | - | - |
E2f | 0.5 | - | ↓ 0.6 | - | - | ↑ 1.4 |
E2f | 2 | - | ↑ 2.2 | - | - | → 1.2 |
G12f | 0.5 | - | - | → 0.7 | - | - |
G12f | 2 | - | - | ↑ 1.7 | - | - |
ν12f | 0.5 | - | - | - | → 0.8 | ↑ 1.4 |
ν12f | 2 | - | - | - | → 1.2 | ↓ 0.1 |
ν23f | 0.5 | - | - | - | - | → 0.8 |
ν23f | 2 | - | - | - | - | - |
Em | 0.5 | - | ↓ 0.5 | - | - | ↓ 0.1 |
Em | 2 | - | ↑ 1.9 | → 1.2 | - | → 1.3 |
νm | 0.5 | - | - | - | → 0.8 | - |
νm | 2 | - | - | → 0.8 | - | → 1.3 |
Method | E1 (GPa) | E2 (GPa) | G12 (GPa) | ν12 | ν23 |
---|---|---|---|---|---|
Uniaxial tension | 148 | - | - | 0.29 | - |
Uniaxial compression | 135 | - | - | 0.29 | - |
Transverse compression | - | 7 | - | - | 0.5 |
Flexural testing | 152 | - | - | - | - |
QSEI [46] | 155 | 7 | 10 | 0.29 | - |
Analytical [20] | 156 | 10 | 5.3 | 0.25 | 0.29 |
RVE FEM | 158 | 9 | 6.8 | 0.25 | 0.34 |
Material | Flexural Strength (MPa) | Apparent ILSS (MPa) |
---|---|---|
Reference | 3120 ± 30 | 93.9 ± 0.2 |
Porous | 3150 ± 132 | 73.1 ± 3.1 |
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Antin, K.-N.; Laukkanen, A.; Andersson, T.; Smyl, D.; Vilaça, P. A Multiscale Modelling Approach for Estimating the Effect of Defects in Unidirectional Carbon Fiber Reinforced Polymer Composites. Materials 2019, 12, 1885. https://doi.org/10.3390/ma12121885
Antin K-N, Laukkanen A, Andersson T, Smyl D, Vilaça P. A Multiscale Modelling Approach for Estimating the Effect of Defects in Unidirectional Carbon Fiber Reinforced Polymer Composites. Materials. 2019; 12(12):1885. https://doi.org/10.3390/ma12121885
Chicago/Turabian StyleAntin, Kim-Niklas, Anssi Laukkanen, Tom Andersson, Danny Smyl, and Pedro Vilaça. 2019. "A Multiscale Modelling Approach for Estimating the Effect of Defects in Unidirectional Carbon Fiber Reinforced Polymer Composites" Materials 12, no. 12: 1885. https://doi.org/10.3390/ma12121885