Interphase Model for Effective Moduli of Nanoparticle-Reinforced Composites
Publication: Journal of Engineering Mechanics
Volume 141, Issue 12
Abstract
A novel interphase model is constructed based on the double-inclusion theory and the Eshelby tensor in a finite domain, which can be used to calculate the effective material properties of three-phase composites. The refinement of the double-inclusion theory takes into account the effect of a finite matrix and that of a finite interphase. In the model proposed, the multiphase composites are reinforced by different material fillers, which are embedded in a matrix with finite size. The general formulations are derived following the method of Eshelby’s equivalent inclusion. The Dirichlet and Neumann Eshelby tensors for a spherical inclusion in a finite spherical domain are applied to the homogenization of composite materials. By the explicit inversions of the fourth-order tensors involved, the relationships between the elastic moduli of transversely isotropic and orthotropic materials are derived, which are then validated through numerical results from the homogenization of several composites. In addition, the interphase and boundary effects on the effective elastic properties of the composites are investigated.
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Acknowledgments
C. Shi is supported by a fellowship from the Faculty Training Project by Shanghai City Municipal Education Commission, and H. Fan is partially supported by a fellowship from Chinese Scholar Council (CSC). There supports are gratefully acknowledged.
References
Aboutajeddine, A., and Neale, K. (2005). “The double-inclusion model: A new formulation and new estimates.” Mech. Mater., 37(2–3), 331–341.
Boutaleb, S., et al. (2009). “Micromechanics-based modelling of stiffness and yield stress for silica/polymer nanocomposites.” Int. J. Solids Struct., 46(7–8), 1716–1726.
Dunn, M. L. (1995). “Elastic moduli of composites reinforced by multiphase particles.” J. Appl. Mech., 62(4), 1023–1028.
Eitan, A., Fisher, F. T., Andrews, R., Brinson, L. C., and Schadler, L. S. (2006). “Reinforcement mechanisms in MWCNT-filled polycarbonate.” Compos. Sci. Technol., 66(9), 1162–1173.
Eshelby, J. D. (1957). “The determination of the elastic field of an ellipsoidal inclusion, and related problems.” Proc. R. Soc. A, 241(1226), 376–396.
Frankland, S. J. V., Caglar, A., Brenner, D. W., and Griebel, M. (2002). “Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube-polymer interfaces.” J. Phys. Chem. B, 106(12), 3046–3048.
Hallal, A., Fardoun, F., Younes, R., and Chehade, F. H. (2011). “Evaluation of longitudinal and transversal Young’s moduli for unidirectional composite material with long fibers.” Adv. Mater. Res., 324, 189–192.
Hill, R. (1963). “Elastic properties of reinforced solids: some theoretical principles.” J. Mech. Phys. Solids, 11(5), 357–372.
Hori, M., and Nemat-Nasser, S. (1994). “Double-inclusion model and overall moduli of multi-phase composites.” J. Eng. Mater. Technol., 116(3), 305.
Huang, M. Z. (2001). “Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites.” Int. J. Solids Struct., 38(22–23), 4147–4172.
Ju, J. W., and Sun, L. Z. (2001). “Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: Micromechanics-based formulation.” Int. J. Solids Struct., 38(2), 183–201.
Li, S., Sauer, R. A., and Wang, G. (2005). “Circular inclusion in a finite elastic domain. I: The Dirichlet-Eshelby problem.” Acta Mech., 179(1–2), 67–90.
Li, S., Sauer, R. A., and Wang, G. (2007a). “The Eshelby tensors in a finite spherical domain—Part I: Theoretical formulations.” J. Appl. Mech., 74(4), 770–783.
Li, S., Wang, G., and Sauer, R. A. (2007b). “The Eshelby tensors in a finite spherical domain—Part II: Applications to homogenization.” J. Appl. Mech., 74(4), 784–797.
Liu, H. T., and Sun, L. Z. (2005). “Multi-scale modeling of elastoplastic deformation and strengthening mechanisms in aluminum-based amorphous nanocomposites.” Acta Mater., 53(9), 2693–2701.
Lu, P., Leong, Y. W., Pallathadka, P. K., and He, C. B. (2013). “Effective moduli of nanoparticle reinforced composites considering interphase effect by extended double-inclusion model—Theory and explicit expressions.” Int. J. Eng. Sci., 73, 33–55.
Mesbah, A., et al. (2009). “Experimental characterization and modeling stiffness of polymer/clay nanocomposites within a hierarchical multiscale framework.” J. Appl. Polym. Sci., 114(5), 3274–3291.
Mori, T., and Tanaka, K. (1973). “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall., 21(5), 571–574.
Nemat-Nasser, S., Lori, M., and Datta, S. K. (1996). “Micromechanics: Overall properties of heterogeneous materials.” J. Appl. Mech., 63(2), 561.
Odegard, G. M., Clancy, T., and Gates, T. (2005). “Modeling of the mechanical properties of nanoparticle/polymer composites.” Polymer, 46(2), 553–562.
Peng, R. D., Zhou, H. W., Wang, H. W., and Mishnaevsky, L. (2012). “Modeling of nano-reinforced polymer composites: Microstructure effect on Young’s modulus.” Comput. Mater. Sci., 60, 19–31.
Shodja, H. M., and Sarvestani, A. S. (2001). “Elastic fields in double inhomogeneity by the equivalent inclusion method.” J. Appl. Mech., 68(1), 3.
Wang, G., Li, S., and Sauer, R. (2005). “Circular inclusion in a finite elastic domain. II: The Neumann-Eshelby problem.” Acta Mech., 179(1–2), 91–110.
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Published In
Journal of Engineering Mechanics
Volume 141 • Issue 12 • December 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Oct 8, 2014
Accepted: Mar 18, 2015
Published online: May 21, 2015
Discussion open until: Oct 21, 2015
Published in print: Dec 1, 2015
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