Abstract
Recognized as a prominent material for engineering applications, carbon fiber-reinforced laminated composites require significant effort to characterize due to their anisotropic structure and viscoelastic nature. Dynamic mechanical analysis has been used to accelerate the testing process by transforming the measured viscoelastic properties to elastic modulus. To expand the transformation to anisotropic materials, artificial neural network approach is used to build the master relationship of the storage modulus in three in-plane directions. Using rotation transformation, the stiffness tensor can be calculated to extrapolate the frequency domain viscoelastic properties in any orientation with respect to the fiber direction. The viscoelastic properties are transformed to time domain relaxation function using the linear relationship of viscoelasticity. Stress response with a certain strain history is predicted and the elastic modulus is extracted. Compared to the experimental flexural test results, the artificial neural network-based method achieved an error of less than 7.3%. The results show that the transformation can predict the anisotropic material behavior at a wide range of temperatures and strain rates.
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References
M. MInus and S. Kumar, JOM 57, 52 (2005). https://doi.org/10.1007/s11837-005-0217-8.
R.A. Sullivan, JOM 58, 77 (2006). https://doi.org/10.1007/s11837-006-0233-3.
L. Peroni, M. Scapin, C. Fichera, D. Lehmhus, J. Weise, J. Baumeister, and M. Avalle, Compos. B 66, 430 (2014). https://doi.org/10.1016/j.compositesb.2014.06.001.
F. Chen, Y. Luo, N.G. Tsoutsos, M. Maniatakos, K. Shahin, and N. Gupta, Adv. Eng. Mater. (2019). https://doi.org/10.1002/adem.201800495.
A.K. Singh, B. Saltonstall, B. Patil, N. Hoffmann, M. Doddamani, and N. Gupta, JOM 70, 310 (2018). https://doi.org/10.1007/s11837-017-2731-x.
F. Chen, G. Mac, and N. Gupta, Mater. Des. 128, 182 (2017). https://doi.org/10.1016/j.matdes.2017.04.078.
A.K. Singh, B. Patil, N. Hoffmann, B. Saltonstall, M. Doddamani, and N. Gupta, JOM 70, 303 (2018). https://doi.org/10.1007/s11837-017-2734-7.
D. Ivaneyko, V. Toshchevikov, and M. Saphiannikova, Polymer 147, 95 (2018). https://doi.org/10.1016/j.polymer.2018.04.057.
Z. Jin, K.P. Pramoda, G. Xu, and S.H. Goh, Chem. Phys. Lett. 337, 43 (2001). https://doi.org/10.1016/S0009-2614(01)00186-5.
L.J. Dooling, M.E. Buck, W.-B. Zhang, and D.A. Tirrell, Adv. Mater. 28, 4651 (2016). https://doi.org/10.1002/adma.201506216.
I. Ivaneiko, V. Toshchevikov, K.W. Stöckelhuber, M. Saphiannikova, and G. Heinrich, Polymer 127, 129 (2017). https://doi.org/10.1016/j.polymer.2017.08.051.
K.P. Sharma, R. Harniman, T. Farrugia, W.H. Briscoe, A.W. Perriman, and S. Mann, Adv. Mater. 28, 1597 (2016). https://doi.org/10.1002/adma.201504740.
P.A. Romero, S.F. Zheng, and A.M. Cuitiño, J. Mech. Phys. Solids 56, 1916 (2008). https://doi.org/10.1016/j.jmps.2007.11.007.
D.D. Luong, D. Pinisetty, and N. Gupta, Compos. B 44, 403 (2013). https://doi.org/10.1016/j.compositesb.2012.04.060.
J.D. Ferry, Dependence of Viscoelastic Behavior on Temperature and Pressure (New York: Wiley, 1980), p. 225.
S.E. Zeltmann, B.R. Bharath Kumar, M. Doddamani, and N. Gupta, Polymer 101, 1 (2016). https://doi.org/10.1016/j.polymer.2016.08.053.
S.E. Zeltmann, K.A. Prakash, M. Doddamani, and N. Gupta, Compos. B 120, 27 (2017). https://doi.org/10.1016/j.compositesb.2017.03.062.
C. Koomson, S.E. Zeltmann, and N. Gupta, Adv. Compos. Hybrid. Mater. 1, 341 (2018). https://doi.org/10.1007/s42114-018-0026-5.
X. Xu and N. Gupta, Polymer 157, 166 (2018). https://doi.org/10.1016/j.polymer.2018.10.036.
X. Xu and N. Gupta, Materialia 4, 221 (2018). https://doi.org/10.1016/j.mtla.2018.09.034.
X. Xu, C. Koomson, M. Doddamani, R.K. Behera, and N. Gupta, Compos. B 159, 346 (2019). https://doi.org/10.1016/j.compositesb.2018.10.015.
X. Xu and N. Gupta, Adv. Theory Simul. (2019). https://doi.org/10.1002/adts.201800131.
E. Vatankhah, D. Semnani, M.P. Prabhakaran, M. Tadayon, S. Razavi, and S. Ramakrishna, Acta Biomater. 10, 709 (2014). https://doi.org/10.1016/j.actbio.2013.09.015.
L.F. Cupertino, O.P.V. Neto, M.A.C. Pacheco, M.B.R. Vellasco, and J.R.M. d’Almeida, Modeling the young modulus of nanocomposites: a neural network approach. in The 2011 International Joint Conference on Neural Networks, San Jose, California, USA (2011). https://doi.org/10.1109/ijcnn.2011.6033415.
Z. Sun, E. Ambrosi, A. Bricalli, and D. Ielmini, Adv. Mater. 30, 1802554 (2018). https://doi.org/10.1002/adma.201802554.
P. Jarosz, J. Kusiak, S. Małecki, P. Morkisz, P. Oprocha, W. Pietrucha, and Ł. Sztangret, JOM 68, 1535 (2016). https://doi.org/10.1007/s11837-016-1916-z.
G. Zhao, J. Yang, J. Chen, G. Zhu, Z. Jiang, X. Liu, G. Niu, Z.L. Wang, and B. Zhang, Adv. Mater. Technol. 4, 1800167 (2019). https://doi.org/10.1002/admt.201800167.
O. Sporns, Adv. Mater. 5, 488 (1993). https://doi.org/10.1002/adma.19930050624.
H. Li, Z. Hu, W. Hu, and L. Hua, JOM 10, 10 (2019). https://doi.org/10.1007/s11837-018-03326-2.
D.J. Armaghani, E. Tonnizam Mohamad, E. Momeni, M. Monjezi, and M. Sundaram Narayanasamy, Arab. J. Geosci. 9, 48 (2015). https://doi.org/10.1007/s12517-015-2057-3.
RS Anupama Upadhyay, OALib J. 1, 1 (2014). https://doi.org/10.4236/oalib.1100903.
R.B. Heslehurst, Compos. Struct. 35, 369 (1996). https://doi.org/10.1016/S0263-8223(96)00042-6.
I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Cambridge, MA: MIT Press, 2016).
O.A. Mohamed, S.H. Masood, and J.L. Bhowmik, Measurement 107, 128 (2017). https://doi.org/10.1016/j.measurement.2017.05.019.
J. Kennedy and R. Eberhart, Particle swarm optimization. in Proceedings of ICNN’95 - International Conference on Neural Networks, Perth, WA, Australia, 1995. https://doi.org/10.1109/icnn.1995.488968.
M. Clerc and J. Kennedy, IEEE Trans. Evolut. Comput. 6, 58 (2002). https://doi.org/10.1109/4235.985692.
I.C. Trelea, Inf. Process. Lett 85, 317 (2003). https://doi.org/10.1016/S0020-0190(02)00447-7.
P.J. Angeline, Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences (Berlin: Springer, 1998).
Z. Jia, T. Li, F.-P. Chiang, and L. Wang, Compos. Sci. Technol. 154, 53 (2018). https://doi.org/10.1016/j.compscitech.2017.11.015.
R.T.H. Zafer Gürdal and Prabhat Hajela, Design and Optimization of Laminated Composite Materials (New York: Wiley, 1999).
H. Markovitz, J. Colloid Interface Sci. 98, 292 (1984). https://doi.org/10.1016/0021-9797(84)90514-9.
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Xu, X., Gupta, N. Artificial Neural Network Approach to Determine Elastic Modulus of Carbon Fiber-Reinforced Laminates. JOM 71, 4015–4023 (2019). https://doi.org/10.1007/s11837-019-03666-7
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DOI: https://doi.org/10.1007/s11837-019-03666-7