Acta Mechanica

, Volume 157, Issue 1–4, pp 113–127 | Cite as

Size effects in the particle-reinforced metal-matrix composites

  • S. H. Chen
  • T. C. Wang
Original Papers


Many experimental observations have shown the influences of particle size on the mechanical propertics of the particle-reinforced metal-matrix composite. However, the conventional theory cannot explain the phenomena because no length scale parameters are included in the conventional theory. In the present paper, the strain gradient theory proposed by Chen and Wang [32] is used, and a systematic research of the particle size effect in the particle-reinforced metal-matrix composite is carried out. Many composite factors, such as the particle size, the particle aspect ratio, the Young's modulus ratio of the particle to the matrix material, particle volume fraction and the strain hardening exponent of the matrix material, are investigated in detail. Two kinds of particle shapes, spheroidal particle and cylindrical particle, are considered to check the strength dependence of the particle shapes. Calculation to the special materials used by Ling [9] has been done, and the calculation results are consistent with the experimental results in Ling [9]. The material length scale parameter is predicted.


Matrix Material Particle Shape Strain Gradient Particle Volume Particle Volume Fraction 
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  1. [1]
    Christman, T., Needleman, A., Suresh, S.: An experimental and numerical study of deformation in metal ceramic composites. Acta Metall. Mater.37, 3029–3050 (1989).Google Scholar
  2. [2]
    Bao, G., Hutchinson, J. W., McMeeking, R. M.: Particle reinforcement of ductile matrices against plastic flow and creep. Acta Metall. Mater.39, 1871–1882 (1991).Google Scholar
  3. [3]
    Corbin, S. F., Wilkinson, D. S.: The influence of particle distribution on the mechanical response of a particulate metal-matrix composite. Acta Metall. Mater.42, 1311–1318 (1994).Google Scholar
  4. [4]
    Boland, F., Colin, C., Salmon, C. et al.: Tensile flow properties of Al-based matrix composites reinforced with a random planar network of continuous metallic fibers. Acta Mater.46, 6311–6323 (1998).Google Scholar
  5. [5]
    Yang, J., Cady, C., Hu, M. S. et al.: Effects of damage on the flow strength and ductility of a ductile Al-alloy reinforced with SiC particulates. Acta Metall. Mater.38, 2613–2619 (1990).Google Scholar
  6. [6]
    Kamat, S. V., Rollett, A. D., Hirth, J. P.: Plastic-deformation in Al-alloy matrix-alumina particulate composites. Scripta Metall. Mater.25, 27–32 (1991).Google Scholar
  7. [7]
    Lloyd, D. J.: Particle-reinforced aluminum and magnesium matrix composite. Int. Mater. Rev.39, 1–23 (1994).Google Scholar
  8. [8]
    Kiser, M. T., Zok, F. W., Wilkinson, D. S.: Plastic flow and fracture of a particulate metal matrix composite. Acta Mater.44, 3465–3476 (1996).Google Scholar
  9. [9]
    Ling, Z.: Deformation behavior and microstructure effect in 2124Al/SuCp composite. J. Comp. Mater.34, 101–115 (2000).Google Scholar
  10. [10]
    Nan, C. W., Clarke, D. R.: The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites. Acta Mater.44, 3801–3811 (1996).Google Scholar
  11. [11]
    Maire, E., Wilkinson, D. S., Embury, D. et al.: Role of damage on the flow and fracture of particulate reinforced alloys and metal matrix composites. Acta Mater.45, 5261–5274 (1997).Google Scholar
  12. [12]
    Ma, Q., Clarke, D. R.: Size dependent hardness in silver single crystals. J. Mat. Res.10, 853–863 (1995).Google Scholar
  13. [13]
    Fleck, N. A., Muller, G. M., Ashby, M. F., Hutchinson, J. W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater.42, 475–487 (1994).Google Scholar
  14. [14]
    Stolken, J. S., Evans, A. G.: A microbend test method for measuring the plasticity length scale. Acta Mater.46, 5109–5115 (1998).Google Scholar
  15. [15]
    Elssner, G., Korn, D., Ruehle, M.: The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals. Scripta Metall. Mater.31, 1037–1042 (1994).Google Scholar
  16. [16]
    Fleck, N. A., Hutchinson, J. W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids41, 1825–1857 (1993).Google Scholar
  17. [17]
    Fleck, N. A., Hutchinson, J. W.: Strain gradient plasticity. Adv. Appl. Mech.33 (Hutchinson, J. W., Wu, T. Y., eds.), pp. 295–361. New York: Academic Press 1997.Google Scholar
  18. [18]
    Gao, H., Huang, Y., Nix, W. D., Hutchinson, J. W.: Mechanism-based strain gradient plasticity-I: theory. J. Mech. Phys. Solids47, 1239–1263 (1999).Google Scholar
  19. [19]
    Wei, Y., Hutchinson, J. W.: Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity. J. Mech. Phys. Solids45, 1253–1273 (1997).Google Scholar
  20. [20]
    Wei, Y.: Particulate size effects in the particle-reinforced metal-matrix composites. Acta Mech. Sin.17, 45–58 (2001).Google Scholar
  21. [21]
    Shu, J. Y., Fleck, N. A.: Strain gradient crystal plasticity: size-dependent deformation of bicrystals. J. Mech. Phys. Solids47, 292–324 (1999).Google Scholar
  22. [22]
    Shu, J. Y., Barlow, L. Y.: Strain gradient effects on microscopic strain field in a metal matrix composite. Int. J. Plast.16, 563–591 (2000).Google Scholar
  23. [23]
    Bassani, J. L., Needleman, A., Giessen, E. Van Der: Plastic flow in a composite: a comparison of nonlocal continuum and discrete dislocation predictions. Int. J. Solids Struct.38, 833–853 (2001).Google Scholar
  24. [24]
    Nix, W. D., Gao, H.: Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids46, 411–425 (1998).Google Scholar
  25. [25]
    Acharya, A., Shawki, T. G.: Thermodynamic restrictions on constitutive equations for second-deformation-gradient inelastic behavior. J. Mech. Phys. Solids43, 1751–1772 (1995).Google Scholar
  26. [26]
    Aifantis, E. C.: On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol.106, 326–330 (1984).Google Scholar
  27. [27]
    Muhlhaus, H. B., Aifantis, E. C.: The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials. Acta Mech.89, 217–231 (1991).Google Scholar
  28. [28]
    Zbib, H., Aifantis, E. C.: On the localization and postlocalization behavior of plastic deformation. Part I. On the initiation of shear bands. Part II. On the evolution and thickness of shear bands. Part III. On the structure and velocity of Portevin-Le Chatelier bands. Res. Mech. 261–277, 279–292, 293–305 (1989).Google Scholar
  29. [29]
    Zbib, H., Aifantis, E. C.: On the gradient-dependent theory of plasticity and shear banding. Acta Mech.92, 209–225 (1992).Google Scholar
  30. [30]
    Acharya, A., Bassani, J. L.: On non-local flow theories that preserve the classical structure of incremental boundary value problems. In: Micromechanics of plasticity and damage of multiphase materials. IUTAM Symposium, Paris, August 29–September 1, 1995.Google Scholar
  31. [31]
    Chen, S. H., Wang, T. C.: A new hardening law for strain gradient plasticity. Acta Mat.48, 3997–4005 (2000).Google Scholar
  32. [32]
    Chen, S. H., Wang, T. C.: A new deformation theory for strain gradient effects. Int. J. Plast. (forthcoming 2002).Google Scholar
  33. [33]
    Chen, S. H., Wang, T. C.: Mode I crack tip with strain gradient effect. Acta Mech. Solida Sin.13, 290–298 (2000).Google Scholar
  34. [34]
    Chen, S. H., Wang, T. C.: Mode I and Mode II crack tip asymptotic fields with strain gradient effects. Acta Mech. Sin.17, 269–280 (2001).Google Scholar
  35. [35]
    Chen, S. H., Wang, T. C.: Finite element solutions for plane strain mode I crack with strain gradient effects. Int. J. Solids Struct. (forthcoming 2002).Google Scholar
  36. [36]
    Chen, S. H., Wang, T. C.: A study of size-dependent microindentation test., (forthcoming).Google Scholar
  37. [37]
    Smyshlyaev, V. P., Fleck, N. A.: The role of strain gradients in the grain size effect for polycrystals. J. Mech. Phys. Solids44, 465–495 (1996).Google Scholar
  38. [38]
    Shu, J. Y., Fleck, N. A.: The prediction of a size effect in microindentation. Int. J. Solids Struct.35, 1363–1383 (1998).Google Scholar
  39. [39]
    Xia, Z. C., Hutchinson, J. W.: Crack tip fields in strain gradient plasticity. J. Mech. Phys. Solids44, 1621–1648 (1996).Google Scholar
  40. [40]
    Shu, J. Y., King, W. E., Fleck, N. A.: Finite elements for materials with strain gradient effects. Int. J. Numer. Methods Eng.44, 373–391 (1999).Google Scholar

Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  • S. H. Chen
    • 1
  • T. C. Wang
    • 1
  1. 1.LNM, Institute of MechanicsChinese Academy of SciencesBeijingP.R. China

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