Abstract
By transforming the governing equations for displacement components into Riccati equations, analytical solutions for displacements, strains and stresses for Representive Volume Elements (RVEs) of particle- and fiber-reinforced composites containing inhomogenous interphases were obtained. The analytical solutions derived here are new and general for power-law variations of the elastic moduli of the inhomogeneous interphases. Given a power exponent, analytical expressions for the bulk moduli of the composites with inhomogenous interphases can be obtained. By changing the power exponent and the coefficients of the power terms, the solutions derived here can be applied to inhomogeneous interphases with many different property profiles. The results show that the modulus variation and the thickness of the inhomogeneous interphase have great effect on the bulk moduli of the composites. The particle will exhibit a sort of “size effect”, if there is an interphase.
Similar content being viewed by others
References
Dai L H, Huang Z P, Wang R. Explicit expressions for bounds for the effective moduli of multiphased composites by the generalized self-consistent method[J].Composites Science and Technology, 1999,59(11):1691–1699.
Zhong Zheng. Elastic moduli of composite materials with soft coatings[J].Acta Mechanica Solida Sinica, 2000,21(4):350–354 (in Chinese).
Wu Y M, Huang Z P, Zhong Yet al., Effective moduli of particle-filled composite with inhomogeneous interphase: Part I—bounds[J].Composites Science and Technology, 2004,64(9):1345–1351.
Zhong Y, Wang J, Wu Y Met al. Effective moduli of particle-filled composite with inhomogeneous interphase: Part II—mapping method and evaluation[J].Composites Science and Technology, 2004,64(9):1353–1362.
Wang W, Jasiuk I. Effective elastic constants of particulate composites with inhomogeneous interphases[J].Journal of Composite Materials, 1998,32(15):1391–1424.
Ding K, Weng G J. The influence of moduli slope of a linearly graded matrix on the bulk moduli of some particle and fiber-reinforced composites[J].Journal of Elasticity, 1999,53(1):1–22.
Jasiuk I, Kouider M W. The effect of an inhomogeneous interphase on the elastic constants of transversely istropic composites[J].Mechanics of Materials, 1993,15(1):53–63.
Christensen R M, Lo K H. Solutions for effective shear properties in three phase sphere and cylinder models[J].Journal of the Mechanics and Physics of Solids, 1979,27(3):315–330.
Hashin Z. The elastic moduli of heterogeneous materials[J].Journal of Applied Mechanics, 1962,29(1):143–150.
Hashin Z, Rosen B W. The elastic moduli of fiber-reinforced materials[J].Journal of Applied Mechanics, 1964,31(2):223–232.
Zheng Q S, Du D X. An explicit and universally applicable estimate for the effective properties of multiphase composites which account for inclusion distribution[J].Journal of the Mechanics and Physics of Solids, 200149(11):2765–2788.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Contributed by HUANG Zhu-ping
Project supported by the National Natural Science Foundation of China (Nos. 10032010, 10072002 and 10372004)
Rights and permissions
About this article
Cite this article
Hui-ling, D., Jian-xiang, W., Zhu-ping, H. et al. Analytical solutions for elastostatic problems of particle-and fiber-reinforced composites with inhomogeneous interphases. Appl Math Mech 26, 336–344 (2005). https://doi.org/10.1007/BF02440084
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02440084
Key words
- inhomogeneous interphase
- particle-reinforced composite
- fiber-reinforced composite
- analytical solution
- bulk modulus