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A new approach to the elastic–plastic stress transfer analysis of metal matrix composites

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Abstract

An analytical approach is proposed for studying the elastic–plastic behavior of short-fiber-reinforced metal matrix composites under tensile loading. In the proposed research, a micromechanical approach is employed, considering an axisymmetric unit cell including one fiber and the surrounding matrix. First, the governing equations and the boundary conditions are derived and the elastic solution is obtained based on some shear-lag-type methods. Since under normal loading conditions and according to the fiber material characteristics, the metal matrix undergoes plastic deformation, while the fiber remains within the elastic region, a plastic deformation is considered for the matrix under each small tensile loading step. Then, applying the successive elastic solutions method, all the plastic strain terms are obtained for the matrix. Thereafter, the elastic–plastic stress transfer behavior of the composite is studied considering this plastic deformation. The results are finally compared with the numerical results obtained from the FE analysis of the considered micromechanical model. The proposed method is capable of predicting all plastic strain terms in the matrix and the stress terms, as well.

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References

  1. Cox, H.L.: The elasticity and strength of paper and other fibrous materials. Br. J. Appl. Phys. 3, 72–79 (1952)

    Article  Google Scholar 

  2. Kelly, A.: Strong Solids, p. 123. Clarendon Press, Oxford (1966)

    Google Scholar 

  3. Fukuda, H., Chou, T.W.: An advanced shear-lag model applicable to discontinuous fiber composites. J. Compos. Mater. 15, 79–91 (1981)

    Article  Google Scholar 

  4. Nardone, V.C., Prewo, K.M.: On the strength of discontinuous silicon carbide reinforced aluminum composites. Scr. Metall. 20, 43–48 (1986)

    Article  Google Scholar 

  5. Karbhari, V.M., Wilkins, D.J.: An engineering modification to the shear-lag model as applied to whisker and particulate reinforced composites. Scr. Metall. 25, 707–712 (1991)

    Article  Google Scholar 

  6. Piggott, M.R.: Load bearing fiber composites, p. 62. Pergamon Press, New York (1980)

    Book  Google Scholar 

  7. Clyne, T.W.: A simple development of the shear lag theory appropriate for composites with a relatively small modulus mismatch. Mater. Sci. Eng. A 122, 183–192 (1989)

    Article  Google Scholar 

  8. Starink, M.J., Syngellakis, S.: Shear lag models for discontinuous composites: fiber end stresses and weak interface layers. Mater. Sci. Eng. A 270, 270–277 (1999)

    Article  Google Scholar 

  9. Gao, X.L., Li, K.: A shear-lag for carbon nanotube-reinforced polymer composites. Int. J. Solids Struct. 42, 1649–1667 (2005)

    Article  MATH  Google Scholar 

  10. Hsueh, C.H.: Elastic load transfer from partially embedded axially loaded fiber to matrix. J. Mater. Sci. Lett. 7(5), 497–500 (1988)

    Article  Google Scholar 

  11. Hsueh, C.H.: Analytical evaluation of interfacial shear strength for fiber-reinforced ceramic composites. J. Am. Ceram. Soc. 71(6), 490–493 (1988)

    Article  Google Scholar 

  12. Hsueh, C.H.: Interfacial debonding and fiber pullout stresses of fiber-reinforced composites. Mater. Sci. Eng. A 123(1), 1–11 (1990)

    Article  Google Scholar 

  13. Hsueh, C.H.: Interfacial debonding and fiber pull-out stresses of fiber-reinforced composites VII: improved analyses for bonded interfaces. Mater. Sci. Eng. A 154, 125–132 (1992)

    Article  Google Scholar 

  14. Hsueh, C.H.: A modified analysis for stress transfer in fiber-reinforced composites with bonded fiber ends. J. Mater. Sci. 30, 219–224 (1995)

    Article  Google Scholar 

  15. Hsueh, C.H., Becher, P.F.: Residual thermal stresses in ceramic composites, Part II: with short fibers. Mater. Sci. Eng. A 212, 29–35 (1996)

    Article  Google Scholar 

  16. Hsueh, C.H., Young, R.J., Yang, X., Becher, P.F.: Stress transfer in a model composite containing a single embedded fiber. Acta Mater. 45(4), 1469–1476 (1997)

    Article  Google Scholar 

  17. Hsueh, C.H., Becher, P.F.: Thermal expansion coefficients of unidirectional fiber-reinforced ceramics. J. Am. Ceram. Soc. 71(10), 438–441 (1988)

    Article  Google Scholar 

  18. Hsueh, C.H.: Modifications of fiber pull-out analysis. Mater. Sci. Lett. 11(12), 1663–1666 (1992)

    Article  Google Scholar 

  19. Hsueh, C.H.: A two-dimensional stress transfer model for platelet reinforcement. Compos. Eng. 4(10), 1033–43 (1994)

    Article  Google Scholar 

  20. Hsueh, C.H., Fuller, E.R., Langer, S.A., Carter, W.C.: Analytical and numerical analyses for two-dimensional stress transfer. Mater. Sci. Eng. A 268, 1–7 (1999)

    Article  Google Scholar 

  21. Jiang, Z., Lian, J., Yang, D., Dong, S.: An analytical study of the influence of thermal residual stresses on the elastic and yield behaviors of short fiber-reinforced metal matrix composites. Mater. Sci. Eng. A 248, 256–275 (1998)

    Article  Google Scholar 

  22. Jiang, Z., Liu, X., Li, G., Lian, J.: A new analytical model for three-dimensional elastic stress field distribution in short fiber composite. Mater. Sci. Eng. A 366, 381–396 (2004)

    Article  Google Scholar 

  23. Nairn, J.A.: On the use of shear-lag methods for analysis of stress transfer in unidirectional composites. Mech. Mater. 26, 63–80 (1997)

    Article  Google Scholar 

  24. Halpin, J.C.: Primer on Composite Materials: Analysis. Technomic, Lancaster (1984)

    Google Scholar 

  25. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241, 376–396 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  26. Jiang, Z., Li, G., Lian, J., Ding, X., Sun, J.: Elastic–plastic stress transfer in short fiber-reinforced metal-matrix composites. Compos. Sci. Technol. 64, 1661–1670 (2004)

    Article  Google Scholar 

  27. Zhao, P., Ji, S.: Refinements of shear-lag model and its applications. Tectonophysics 279, 37–53 (1997)

    Article  Google Scholar 

  28. Ji, B., Wang, T.: Plastic constitutive behavior of short-fiber/particle reinforced composites. Int. J. Plast. 19, 565–581 (2003)

    Article  MATH  Google Scholar 

  29. You, L.H.: Effect of elastic–plastic matrix on thermo-mechanical response of continuous anisotropic fiber-reinforced composites. Compos. Sci. Technol. 62, 2209–2218 (2002)

    Article  Google Scholar 

  30. You, L.H., You, X.Y.: A unified numerical approach for thermal analysis of transversely isotropic fiber-reinforced composites containing inhomogeneous interphase. Compos. Part A 36, 728–738 (2005)

    Article  Google Scholar 

  31. You, L.H., You, X.Y., Zheng, Z.Y.: Thermomechanical analysis of elastic–plastic fibrous composites comprising an inhomogeneous interphase. Comput. Mater. Sci. 36, 440–450 (2006)

    Article  Google Scholar 

  32. Mahesh, S., Hanan, J.C., Ustundag, E., Beyerlein, I.J.: Shear-lag model for a single fiber metal matrix composite with an elasto-plastic matrix and a slipping interface. Int. J. Solids Struct. 41, 4197–4218 (2004)

    Article  MATH  Google Scholar 

  33. Okabe, T., Takeda, N., Kamoshida, Y., Shimizu, M., Curtin, W.A.: A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites. Compos. Sci. Technol. 61, 1773–1787 (2001)

    Article  Google Scholar 

  34. Xia, Z., Curtin, W.A., Okabe, T.: Green’s function vs. shear-lag models of damage and failure in fiber composites. Compos. Sci. Technol. 62, 1279–1288 (2002)

    Article  Google Scholar 

  35. Xia, Z., Okabe, T., Curtin, W.A.: Shear-lag versus finite element models for stress transfer in fiber-reinforced composites. Compos. Sci. Technol. 62, 1141–1149 (2002)

    Article  Google Scholar 

  36. Nishikawa, M., Okabe, T., Takeda, N., Curtin, W.A.: Micromechanics of the fragmentation process in single-fiber composites. Model. Simul. Mater. Sci. Eng. 16, 055009 (2008)

    Article  Google Scholar 

  37. Mendelson, A.: Plasticity: Theory and Application. The MacMillan Company, New York (1968)

  38. Mondali, M., Abedian, A.: An analytical model for stress analysis of short fiber composites in power law creep matrix. Int. J. Non-Linear Mech. 57, 39–49 (2013)

    Article  Google Scholar 

  39. ASM International, Atlas of Stress–Strain Curves, 2nd edn. Materials park, OH (2002)

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Authors and Affiliations

  1. Aerospace Engineering Department, Sharif University of Technology, P.O. Box: 11365-8639, Azadi Ave., Tehran, Iran

    S. Khosoussi & A. Abedian

  2. Department of Mechanical and Aerospace Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran

    M. Mondali

Authors
  1. S. Khosoussi
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  2. M. Mondali
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  3. A. Abedian
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Correspondence to S. Khosoussi.

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Khosoussi, S., Mondali, M. & Abedian, A. A new approach to the elastic–plastic stress transfer analysis of metal matrix composites. Arch Appl Mech 85, 1701–1717 (2015). https://doi.org/10.1007/s00419-015-1013-8

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  • DOI: https://doi.org/10.1007/s00419-015-1013-8

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