Skip to main content
Log in

A study on the plastic properties of unidirectional nanocomposites with interface energy effects

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, for obtaining an overall size-dependent yield function for nanocomposites containing aligned cylindrical nanofibers, the effects of interface residual stress and interface elasticity are taken into account within a micromechanical framework. Toward this goal, the modified Hill’s condition is used, and then, in order to consider effects of the interface residual stress, strains are decomposed into two parts, a part due to the external loadings and the other due to the interface residual stress. Next, utilizing the field fluctuation method, an overall yield function containing effective elastic constants of the material is derived and then simplified for practical loading conditions. Moreover, a secant modulus scheme is adopted to examine the overall nonlinear behavior of the material in plastic deformation. Finally, by some numerical examples, it is shown that the interface stress, including the interface residual stress, makes the yield strength and plastic deformation of the metal matrix nanocomposites dependent on the nanofiber size, in contrast to the classical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bakshi S., Lahiri D., Agarwal A.: Carbon nanotube reinforced metal matrix composites—A review. Int. Mater. Rev. 55, 41–64 (2010)

    Article  Google Scholar 

  2. Cammarata R.C.: Surface and interface stress effects in thin films. Prog. Surf. Sci. 46, 1–38 (1994)

    Article  Google Scholar 

  3. Sharma P., Ganti S., Bhate N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82, 535–537 (2003)

    Article  Google Scholar 

  4. Duan H.L., Wang J., Karihaloo B.L., Huang Z.P.: Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Mater. 54, 2983–2990 (2006)

    Article  Google Scholar 

  5. Chen T., Dvorak G.J., Yu C.C.: Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech. 188, 39–54 (2007)

    Article  MATH  Google Scholar 

  6. Mogilevskaya S.G., Crouch S.L., Stolarski H.K., Benusiglio A.: Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects. Int. J. Solids Struct. 47, 407–418 (2010)

    Article  MATH  Google Scholar 

  7. Mishra S., Sonawane S.H., Singh R.P.: Studies on characterization of nano CaCO3 prepared by the in situ deposition technique and its application in PP-nano CaCO3 composites. J. Polym. Sci. B Polym. Phys. 43, 107–113 (2005)

    Article  Google Scholar 

  8. Cho J., Joshi M.S., Sun C.T.: Effect of inclusion size on mechanical properties of polymeric composites with micro and nano particles. Compos. Sci. Technol. 66, 1941–1952 (2006)

    Article  Google Scholar 

  9. Mori T., Tanaka K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Met. 21, 571–574 (1973)

    Article  Google Scholar 

  10. Christensen R.M., Lo K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)

    Article  MATH  Google Scholar 

  11. Hashin Z.: Analysis of composite materials—a survey. J. Appl. Mech. 50, 481–505 (1983)

    Article  MATH  Google Scholar 

  12. Nemat-Nasser S., Hori M.: Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, Amsterdam (1999)

    Google Scholar 

  13. Qu J., Cherkaoui M.: Fundamentals of Micromechanics of Solids. Wiley, New York (2006)

    Book  Google Scholar 

  14. Gurtin M.E., Ian Murdoch A.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)

    Article  MATH  Google Scholar 

  15. Duan H.L., Wang J., Karihaloo B.L.: Theory of elasticity at the nanoscale. Adv. Appl. Mech. 42, 1–68 (2009)

    Article  Google Scholar 

  16. Assadi A., Farshi B.: Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech. 222, 27–39 (2011)

    Article  MATH  Google Scholar 

  17. Yang Q., Liu J.X., Fang X.Q.: Dynamic stress in a semi-infinite solid with a cylindrical nano-inhomogeneity considering nanoscale microstructure. Acta Mech. 223, 879–888 (2012)

    Article  MathSciNet  Google Scholar 

  18. Gao W., Yu S., Huang G.: Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17(4), 1118–1122 (2006)

    Article  Google Scholar 

  19. Assadi, A., Farshi, B.: Vibration characteristics of circular nanoplates. J. Appl. Phys. 108, 074312-1–074312-5 (2010)

  20. Zhang, W.X., Wang, T.J.: Effect of surface energy on the yield strength of nanoporous materials. Appl. Phys. Lett. 90, 063104-1–063104-3 (2007)

  21. Chen H., Liu X., Hu G.: Overall plasticity of micropolar composites with interface effect. Mech. Mater. 40, 721–728 (2008)

    Article  Google Scholar 

  22. Zhang W.X., Wang T.J., Chen X.: Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites. Int. J. Plast. 26, 957–975 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Goudarzi T., Avazmohammadi R., Naghdabadi R.: Surface energy effects on the yield strength of nanoporous materials containing nanoscale cylindrical voids. Mech. Mater. 42, 852–862 (2010)

    Article  Google Scholar 

  24. Moshtaghin A.F., Naghdabadi R., Asghari M.: Effects of surface residual stress and surface elasticity on the overall yield surfaces of nanoporous materials with cylindrical nanovoids. Mech. Mater. 51, 74–87 (2012)

    Article  Google Scholar 

  25. Chen, T., Chiu, M.S., Weng, C.N.: Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. J. Appl. Phys. 100, 074308-1–074308-5 (2006)

    Google Scholar 

  26. Qiu Y.P., Weng G.J.: A theory of plasticity for porous materials and particle-reinforced composites. J. Appl. Mech. 59, 261–268 (1992)

    Article  MATH  Google Scholar 

  27. Hu G.: A method of plasticity for general aligned spheroidal void or fiber-reinforced composites. Int. J. Plast. 12, 439–449 (1996)

    Article  MATH  Google Scholar 

  28. Qiu Y.P., Weng G.J.: Plastic potential and yield function of porous materials with aligned and randomly oriented spheroidal voids. Int. J. Plast. 9, 271–290 (1993)

    Article  MATH  Google Scholar 

  29. Hashin Z., Rosen B.W.: The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 31, 223–232 (1964)

    Article  Google Scholar 

  30. Chen X.L., Liu Y.J.: Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites. Comput. Mater. Sci. 29, 1–11 (2004)

    Article  Google Scholar 

  31. Namilae S., Chandra N.: Multiscale model to study the effect of interfaces in carbon nanotube-based composites. J. Eng. Mater. Technol. 127, 222–232 (2005)

    Article  Google Scholar 

  32. Lim C.W., Li Z.R., He L.H.: Size dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress. Int. J. Solids Struct. 43, 5055–5065 (2006)

    Article  MATH  Google Scholar 

  33. Chen T.: Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta Mech. 196, 205–217 (2008)

    Article  MATH  Google Scholar 

  34. Pindera M.J., Aboudi J.: Micromechanical analysis of yielding of metal matrix composites. Int. J. Plast. 4(3), 195–214 (1988)

    Article  Google Scholar 

  35. Montazeri A., Naghdabadi R.: Investigating the effect of carbon nanotube defects on the column and shell buckling of carbon nanotube-polymer composites using multiscale modeling. Int. J. Multiscale Comput. Eng. 7, 431–444 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Naghdabadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moshtaghin, A.F., Naghdabadi, R. & Asghari, M. A study on the plastic properties of unidirectional nanocomposites with interface energy effects. Acta Mech 224, 789–809 (2013). https://doi.org/10.1007/s00707-012-0780-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0780-3

Keywords

Navigation