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Equivalent inclusions in micromechanics with interface energy effect

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Abstract

In order to apply classical micromechanics in predicting the effective prop-erties of nanocomposites incorporating interface energy, a concept of equivalent inclusion (EI) is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this pa-per, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method (MTM) and the generalized self-consistent method (GSCM). However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites.

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References

  1. Hashin, Z. Thin interphase/imperfect interface in elasticity with application to coated fiber composites. Journal of the Mechanics and Physics of Solids, 50(12), 2509–2537 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Duan, H. L., Wang, J., Huang, Z. P., and Karihaloo, B. L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. Journal of the Mechanics and Physics of Solids, 53(7), 1574–1596 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, T., Dvorak, G. J., and Yu, C. C. Size-dependent elastic properties of unidirectional nanocomposites with interface stresses. Acta Mechanica, 188(1/2), 39–54 (2007)

    Article  MATH  Google Scholar 

  4. Quang, H. L. and He, Q. C. Estimation of the effective thermoelastic moduli of fibrous nanocomposites with cylindrically anisotropic phases. Archive of Applied Mechanics, 79(3), 225–248 (2009)

    Article  MATH  Google Scholar 

  5. Huang, R. C. and Chen, Y. Q. Effect of residual interface stress on effective thermal expansion coefficient of particle-filled thermoelasticnanocomposite. Applied Mathematics and Mechanics (English Edition), 32(11), 1377–1388 (2011) DOI 10.1007/s10483-011-1508-9

    Article  MATH  MathSciNet  Google Scholar 

  6. Xu, Y., He, Q. C., and Gu, S. T. Effective elastic moduli of fiber-reinforced composites with interfacial displacement and stress jumps. International Journal of Solids and Structures, 80, 146–157 (2016)

    Article  Google Scholar 

  7. Chen, Y. Q., Zhang, Z. G., Huang, R. C., and Huang, Z. P. Effect of residual interface stress on thermo-elastic properties of unidirectional fiber-reinforced nanocomposites. International Journal of Mechanical Sciences, 113, 133–147 (2016)

    Article  Google Scholar 

  8. Hashin, Z. Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials, 8(4), 333–348 (1990)

    Article  Google Scholar 

  9. Dai, L. H., Huang, Z. P., and Wang, R. An explicit expression of the effective moduli for composite materials filled with coated inclusions. Acta Mechanica Sinica, 14(1), 37–52 (1998)

    Article  Google Scholar 

  10. Garboczi, E. J. and Berryman, J. G. Elastic moduli of a material containing composite inclusions: effective medium theory and finite element computations. Mechanics of Materials, 33(8), 455–470 (2001)

    Article  Google Scholar 

  11. Wu, Y. M., Huang, Z. P., Zhong, Y., and Wang, J. Effective moduli of particle-filled composite with inhomogeneous interphase: part I, bounds. Composites Science and Technology, 64(9), 1345–1351 (2004)

    Article  Google Scholar 

  12. Zhong, Y., Wang, J., Wu, Y. M., and Huang, Z. P. Effective moduli of particle-filled composite with inhomogeneous interphase: part II, mapping method and evaluation. Composites Science and Technology, 64(9), 1353–1362 (2004)

    Article  Google Scholar 

  13. Shen, L. and Li, J. Homogenization of a fiber/sphere with an inhomogeneous interphase for the effective elastic moduli of composites. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 461(2057), 1475–1504 (2005)

    Article  Google Scholar 

  14. Lombardo, N. Effect of an inhomogeneous interphase on the thermal expansion coefficient of a particulate composite. Composites Science and Technology, 65(14), 2118–2128 (2005)

    Article  Google Scholar 

  15. Sevostianov, I. and Kachanov, M. Effect of interphase layers on the overall elastic and conductive properties of matrix composites, applications to nanosize inclusion. International Journal of Solids and Structures, 44(3), 1304–1315 (2007)

    Article  MATH  Google Scholar 

  16. Duan, H. L., Yi, X., Huang, Z. P., and Wang, J. A unified scheme for prediction of effective moduli of multiphase composites with interface effects, part I: theoretical framework. Mechanics of Materials, 39(1), 81–93 (2007)

    Article  Google Scholar 

  17. Nguyen, T. K. and Pham, D. C. Equivalent-inclusion approach and effective medium estimates for elastic moduli of two-dimensional suspensions of compound inclusions. Philosophical Magazine, 94(36), 4138–4156 (2014)

    Article  Google Scholar 

  18. Chen, Y. Q., Huang, R. C., and Huang, Z. P. Effect of residual interface stresses on effective specific heats of multiphase thermoelastic nanocomposites. Acta Mechanica, 225(4/5), 1107–1119 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  19. Paulino, G. H., Yin, H. M., and Sun, L. Z. Micromechanics-based interfacial debonding model for damage of functionally graded materials with particle interactions. International Journal of Damage Mechanics, 15(3), 267–288 (2006)

    Article  Google Scholar 

  20. Liu, H. T., Sun, L. Z., and Ju, J. W. Elastoplastic modeling of progressive interfacial debonding for particle-reinforced metal-matrix composites. Acta Mechanica, 181(1), 1–17 (2006)

    Article  MATH  Google Scholar 

  21. Huang, Z. P. and Sun, L. Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis. Acta Mechanica, 190(1-4), 151–163 (2007)

    Article  MATH  Google Scholar 

  22. Huang, Z. P. and Wang, J. Micromechanics of nanocomposites with interface energy effect. Handbook of Micromechanics and Nanomechanics (eds. Li, S. F. and Gao, X. L.), Taylor & Francis Group, Boca Raton, 303–348 (2013)

    Google Scholar 

  23. Huang, Z. P. and Wang, J. Micromechanics of nanocomposites with interface energy effect. Proceedings of IUTAM Symposium on Mechanical Behavior and Micro-Mechanics of Nanostructured Materials (eds. Bai, Y. L., Zheng, Q. S., and Wei, Y. G.), Springer, Beijing, 51–59 (2007)

    Chapter  Google Scholar 

  24. Huang, Z. P. and Wang, J. A theory of hyperelasticity of multiphase media with surface/interface energy effect. Acta Mechanica, 182(3/4), 195–210 (2006)

    Article  MATH  Google Scholar 

  25. Hill, R. Theory of mechanical properties of fibre-strengthened materials I, elastic behavior. Journal of the Mechanics and Physics of Solids, 12(4), 199–222 (1964)

    Article  MathSciNet  Google Scholar 

  26. Christensen, R. M. Mechanics of Composite Materials, John Wiley & Sons, New York (1979)

    Google Scholar 

  27. Lurie, A. I. Three-dimensional Problems of Theory of Elasticity, Interscience Publisher, New York (1964)

    Google Scholar 

  28. Dai, L. H., Huang, Z. P., and Wang, R. Explicit expressions for bounds for the effective moduli of multi-phased composites by the generalized self-consistent method. Composites Science and Technology, 59(11), 1691–1699 (1999)

    Article  Google Scholar 

  29. Qu, J. and Cherkaoui, M. Fundamentals of Micromechanics of Solids, Wiley, Hoboken (2006)

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Zhenguo Zhang, Yongqiang Chen & Zhuping Huang

Authors
  1. Zhenguo Zhang
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  2. Yongqiang Chen
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  3. Zhuping Huang
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Correspondence to Yongqiang Chen.

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Project supported by the National Natural Science Foundation of China (Nos. 11272007 and 11332001)

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Zhang, Z., Chen, Y. & Huang, Z. Equivalent inclusions in micromechanics with interface energy effect. Appl. Math. Mech.-Engl. Ed. 38, 1497–1516 (2017). https://doi.org/10.1007/s10483-017-2276-9

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  • DOI: https://doi.org/10.1007/s10483-017-2276-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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