Multiscale Numerical Modeling of 2D C/C Composites Considering Pore Size Distribution
Publication: Journal of Aerospace Engineering
Volume 37, Issue 4
Abstract
This study proposes a multiscale numerical modeling procedure to evaluate the elastic properties of two-dimensional (2D) eight-harness satin woven carbon/carbon (C/C) composites. The multiscale modeling technique consists of analysis at the microlevel and mesolevel. In microscale analysis, a 3D representative volume element (RVE) of C/C composite with carbon fiber, pyrolytic carbon, and pores is considered. The microstructure of the C/C composite is analyzed using scanning electron microscope (SEM) images. Statistical characterization of pore distribution inside the C/C composite is performed, and different probability density functions are generated for pores’ number, area, and aspect ratio inside the C/C composite. Carbon fibers and pores are inserted in the 3D RVE using the RSA algorithm. The size and shape of the pores inserted in 3D RVE are based on the probability density functions generated. Effective elastic properties of C/C composite at the microscale are computed by finite element analysis (FE) based homogenization and taken as input for the next level of homogenization. The RVE at mesoscale is modeled using the information from SEM images, and FE-based homogenization is performed to compute the effective elastic properties of 8HS woven C/C composite. The effective elastic properties obtained from the numerical study are validated with the results of the uniaxial tensile test performed on 2D C/C composite. The effect of fiber volume fraction, yarn volume fraction, and porosity on elastic properties of 2D 8HS woven C/C composite are also assessed and presented in this study.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors are thankful to VSSC, ISRO for providing C/C composite samples. Nanoindentation tests were performed at CMTI Bengaluru. Uniaxial tensile tests were performed at BMSCE Bengaluru.
References
Adumitroaie, A., and E. J. Barbero. 2011. “Beyond plain weave fabrics–I. Geometrical model.” Compos. Struct. 93 (5): 1424–1432. https://doi.org/10.1016/j.compstruct.2010.11.014.
ASTM. 2008. Standard test method for tensile properties of polymer matrix composite materials. ASTM D3039/D3039M. West Conshohocken, PA: ASTM.
ASTM. 2015. Standard test method for monotonic tensile behavior of continuous fiber-reinforced advanced ceramics with solid rectangular cross-section test specimens at ambient temperature. ASTM C1275-18. West Conshohocken, PA: ASTM.
Benveniste, Y. 1987. “A new approach to the application of Mori-Tanaka’s theory in composite materials.” Mech. Mater. 6 (2): 147–157. https://doi.org/10.1016/0167-6636(87)90005-6.
Blacklock, M., and D. R. Hayhurst. 2011. “Multi-axial failure of ceramic matrix composite fiber tows.” J. Appl. Mech. 78 (3): 031017. https://doi.org/10.1115/1.4002814.
Böhm, H. J., A. Eckschlager, and W. Han. 2002. “Multi-inclusion unit cell models for metal matrix composites with randomly oriented discontinuous reinforcements.” Comput. Mater. Sci 25 (1–2): 42–53. https://doi.org/10.1016/S0927-0256(02)00248-3.
Chao, X., L. Qi, J. Cheng, W. Tian, S. Zhang, and H. Li. 2018. “Numerical evaluation of the effect of pores on effective elastic properties of carbon/carbon composites.” Compos. Struct. 196 (Jul): 108–116. https://doi.org/10.1016/j.compstruct.2018.05.014.
Davies, I. J., and R. D. Rawlings. 1999. “Mechanical properties in compression of CVI-densified porous carbon/carbon composite.” Compos. Sci. Technol. 59 (1): 97–104. https://doi.org/10.1016/S0266-3538(98)00059-1.
Dixit, A., and H. S. Mali. 2013. “Modeling techniques for predicting the mechanical properties of woven-fabric textile composites: A review.” Mech. Compos. Mater. 49 (1): 1–20. https://doi.org/10.1007/s11029-013-9316-8.
Drago, A., and M. J. Pindera. 2007. “Micro-macromechanical analysis of heterogeneous materials: Macroscopically homogeneous vs periodic microstructures.” Compos. Sci. Technol. 67 (6): 1243–1263. https://doi.org/10.1016/j.compscitech.2006.02.031.
Fitzer, E. 1987. “The future of carbon-carbon composites.” Carbon 25 (May): 163–190. https://doi.org/10.1016/0008-6223(87)90116-3.
Ge, J., L. Qi, X. Chao, Y. Xue, X. Hou, and H. Li. 2021. “The effects of interphase parameters on transverse elastic properties of carbon–carbon composites based on FE model.” Compos. Struct. 268 (Jul): 113961. https://doi.org/10.1016/j.compstruct.2021.113961.
Ge, J., L. Qi, W. Tian, X. Chao, W. Li, and H. Li. 2023. “Numerical evaluation of effective elastic properties of CVI-C/C composites considering anisotropic matrix.” Compos. Struct. 306 (Feb): 116561. https://doi.org/10.1016/j.compstruct.2022.116561.
Gommers, B., I. Verpoest, and P. V. Houtte. 1998. “The Mori–Tanaka method applied to textile composite materials.” Acta Mater. 46 (6): 2223–2235. https://doi.org/10.1016/S1359-6454(97)00296-6.
Gusev, A., M. Heggli, H. R. Lusti, and P. J. Hine. 2002. “Orientation averaging for stiffness and thermal expansion of short fiber composites.” Adv. Eng. Mater. 4 (12): 931–933. https://doi.org/10.1002/adem.200290008.
Gusev, A. A. 1997. “Representative volume element size for elastic composites: A numerical study.” J. Mech. Phys. Solids 45 (9): 1449–1459. https://doi.org/10.1016/S0022-5096(97)00016-1.
Hatta, H., K. Goto, S. Ikegaki, I. Kawahara, M. S. Aly-Hassan, and H. Hamada. 2005. “Tensile strength and fiber/matrix interfacial properties of 2D- and 3D-carbon/carbon composites.” J. Eur. Ceram. Soc. 25 (4): 535–542. https://doi.org/10.1016/j.jeurceramsoc.2004.02.014.
Kari, S., H. Berger, and U. Gabbert. 2007. “Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites.” Comput. Mater. Sci 39 (1): 198–204. https://doi.org/10.1016/j.commatsci.2006.02.024.
Liu, L., and Z. Huang. 2014. “A note on Mori-Tanaka’s method.” Acta Mech. Solida Sin. 27 (3): 234–244. https://doi.org/10.1016/S0894-9166(14)60033-1.
Martin, J. 2006. “Composite materials.” In Materials for engineering, 185–215. Cambridge, UK: Woodhead Publishing Limited.
Ogin, S. L., P. Brøndsted, and J. Zangenberg. 2016. “Composite materials: Constituents, architecture, and generic damage.” In Modeling damage, fatigue and failure of composite materials, 3–23. Sawston, UK: Woodhead Publishing.
Oku, T. 2003. “Carbon/Carbon composites and their properties.” In Carbon alloys: Novel concepts to develop carbon science and technology, 523–544. Amsterdam, Netherlands: Elsevier.
Park, S. J., and M. K. Seo. 2011. “Types of composites.” Interface Sci. Technol. 18 (May): 501–629. https://doi.org/10.1016/B978-0-12-375049-5.00007-4.
Piat, R., T. Böhlke, S. Dietrich, J. M. Gebert, and A. Wanner. 2009. “Modeling of effective elastic properties of carbon/carbon laminates.” In Proc., ICCM Int. Conf. on Composite Materials. Edinburgh, UK: International Conference on Composite Materials.
Piat, R., I. Tsukrov, N. Mladenov, M. Guellali, R. Ermel, T. Beck, E. Schnack, and M. J. Hoffmann. 2006. “Material modeling of the CVI-infiltrated carbon felt II. statistical study of the microstructure, numerical analysis and experimental validation.” Compos. Sci. Technol. 66 (15): 2769–2775. https://doi.org/10.1016/j.compscitech.2006.03.003.
Qi, L., X. Chao, W. Tian, W. Ma, and H. Li. 2018. “Numerical study of the effects of irregular pores on transverse mechanical properties of unidirectional composites.” Compos. Sci. Technol. 159 (May): 142–151. https://doi.org/10.1016/j.compscitech.2018.02.020.
Rao, M. V., P. Mahajan, and R. K. Mittal. 2008. “Effect of architecture on mechanical properties of carbon/carbon composites.” Compos. Struct. 83 (2): 131–142. https://doi.org/10.1016/j.compstruct.2007.04.003.
Searles, K., G. Odegard, and M. Kumosa. 2001. “Micro- and mesomechanics of 8-harness satin woven fabric composites: I–evaluation of elastic behavior.” Composites, Part A 32 (11): 1627–1655. https://doi.org/10.1016/S1359-835X(00)00181-0.
Sharma, R., P. Mahajan, and R. K. Mittal. 2013. “Elastic modulus of 3D carbon/carbon composite using image-based finite element simulations and experiments.” Compos. Struct. 98 (Apr): 69–78. https://doi.org/10.1016/j.compstruct.2012.11.019.
Sheehan, J. E., K. W. Buesking, and B. J. Sullivan. 1994. “Carbon-carbon composites.” Annu. Rev. Mater. Sci. 24 (Feb): 19–44. https://doi.org/10.1146/annurev.ms.24.080194.000315.
Sudhir, A., A. M. Nagaraja, and S. Gururaja. 2014. “Effective mechanical properties of carbon-carbon composites.” In Vol. 46421 of ASME international mechanical engineering congress and exposition, V001T01A017. Reston, VA: ASCE.
Sun, C. T., and R. S. Vaidya. 1996. “Prediction of composite properties from a representative volume element.” Compos. Sci. Technol. 56 (2): 171–179. https://doi.org/10.1016/0266-3538(95)00141-7.
Tang, C., M. Blacklock, and D. Hayhurst. 2011. “Stress–strain response and thermal conductivity degradation of ceramic matrix composite fiber tows in 0–90° uni-directional and woven composites.” J. Compos. Mater. 45 (14): 1461–1482. https://doi.org/10.1177/0021998310383726.
Tran, V. P., S. Brisard, J. Guilleminot, and K. Sab. 2018. “Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites.” Int. J. Solids Struct. 146 (Aug): 55–68. https://doi.org/10.1016/j.ijsolstr.2018.03.020.
Trias, D., J. Costa, A. Turon, and J. E. Hurtado. 2006. “Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers.” Acta Mater. 54 (13): 3471–3484. https://doi.org/10.1016/j.actamat.2006.03.042.
Windhorst, T., and G. Blount. 1997. “Carbon-carbon composites: A summary of recent developments and applications.” Mater. Des. 18 (1): 11–15. https://doi.org/10.1016/S0261-3069(97)00024-1.
Xu, Y., P. Zhang, H. Lu, and W. Zhang. 2015. “Hierarchically modeling the elastic properties of 2D needled carbon/carbon composites.” Compos. Struct. 133 (Dec): 148–156. https://doi.org/10.1016/j.compstruct.2015.07.081.
Yang, Z., and H. Yan. 2020. “Multiscale modeling and failure analysis of an 8-harness satin woven composite.” Compos. Struct. 242 (Jun): 112186. https://doi.org/10.1016/j.compstruct.2020.112186.
Zhang, D., and D. Hayhurst. 2014. “Prediction of stress–strain and fracture behaviour of an 8-Harness satin weave ceramic matrix composite.” Int. J. Solids Struct. 51 (21–22): 3762–3775. https://doi.org/10.1016/j.ijsolstr.2014.07.010.
Zhang, Y., and Z. Zhou. 2022. “Experimental and multiscale numerical investigation on failure behavior of satin woven carbon/carbon composites subjected to pin-loading.” Int. J. Mech. Sci. 219 (Apr): 107129. https://doi.org/10.1016/j.ijmecsci.2022.107129.
Zhong, R., and K. Wille. 2016. “Equal arc segment method for averaging data plots exemplified for averaging stress versus strain curves of pervious concrete.” J. Mater. Civ. Eng. 28 (1): 04015071. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001345.
Information & Authors
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Published In
Journal of Aerospace Engineering
Volume 37 • Issue 4 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 18, 2023
Accepted: Dec 14, 2023
Published online: Mar 18, 2024
Published in print: Jul 1, 2024
Discussion open until: Aug 18, 2024
ASCE Technical Topics:
- Analysis (by type)
- Composite materials
- Design (by type)
- Elastic analysis
- Engineering fundamentals
- Engineering materials (by type)
- Finite element method
- Materials engineering
- Methodology (by type)
- Models (by type)
- Multiscale methods
- Numerical analysis
- Numerical methods
- Numerical models
- Structural analysis
- Structural design
- Structural engineering
- Two-dimensional models
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