Skip to main content
SpringerLink
Log in

Strain gradients and continuum modeling of size effect in metal matrix composites

  • Original Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Constitutive modeling for the particle size effect on the strength of particulate-reinforced metal matrix composites is investigated. The approach is based on a gradient-dependent theory of plasticity that incorporates strain gradients into the expression of the flow stress of matrix materials, and a finite unit cell technique that is used to calculate the overall flow properties of composites. It is shown that the strain gradient term introduces a spatial length scale in the constitutive equations for composites, and the dependence of the flow stress on the particle size/spacing can be obtained. Moreover, a nondimensional analysis along with the numerical result yields an explicit relation for the strain gradient coefficient in terms of particle size, strain, and yield stress. Typical results for aluminum matrix composites with ellipsoidal particles are calculated and compare well with data measured experimentally.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kamat, S. V., Hirth, J. P., Mehrabian, R.: Mechanical properties of particulate-reinforced aluminummatrix composites. Acta Metall. Mater.37, 2395–2402 (1991).

    Google Scholar 

  2. Kamat, S. V., Rollet, A. D., Hirth, J. P.: Plastic deformation in Al-alloy matrix-alumina particulate composites. Scripta Metal. Mater.25, 27–32 (1991).

    Google Scholar 

  3. Brown, L. M.: Precipitation and dispersion hardening. In: Strength of metals and alloys (Haasen, P., Gerold, V., Kostorz, G., eds.), pp. 1551–1571. New York: Pergamon Press 1980.

    Google Scholar 

  4. Ashby, M. F.: The deformation of plastically non-homogeneous alloys. In: Strengthening methods in crystals (Kelly, A., Nicholson, R. B. eds.), p. 184. Amsterdam: Elsevier 1980.

    Google Scholar 

  5. Rhee, M., Hirth, J. P., Zbib, H. M.: A superdislocation model for the strengthening of metal matrix composites and the initiation and propagation of shear bands. Acta Metall. Mater.42, 2645–2655 (1994).

    Google Scholar 

  6. Rhee, M., Hirth, J. P., Zbib, H. M.: On the bowed out tilt wall model of flow stress and size effects in metal matrix composites. Scripta Metall. Mater.31, 1321–1324 (1994).

    Google Scholar 

  7. Li, J., Weng, G. J.: Micromechanical determination of the viscoplastic behavior of a metal-matrix composite. In: Inelasticity and micromechanics of metal matrix composites (Voyiadjis, G. Z., Ju, J. W., eds.), pp. 213–227. Amsterdam: Elsevier 1994.

    Google Scholar 

  8. Ju, J. W., Tseng, K. H.: Effective elastoplastic behavior of two-phase metal matrix composites: micromechanics and computational algorithms. In: Inelasticity and micromechanics of metal matrix composites (Voyiadjis, G. Z., Ju, J. W., eds.), pp. 121–141. Amsterdam: Elsevier 1994.

    Google Scholar 

  9. Ponte Castaneda, P.:New variational principles in plasticity and their application to composite materials. J. Mech. Phys. Solids40, 1757–1788 (1992).

    Google Scholar 

  10. Lee, B. J., Mear, M. E.: Effective properties of power-law solids containing elliptical inhomogeneities: Part I: Rigid inclusions. Mech. Mater.13, 313–336 (1992).

    Google Scholar 

  11. 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 

  12. Zbib, H. M., Zhu, H. T.: On the mechanics of plastic deformation in metal-matrix composites. In: Inelasticity and micromechanics of metal matrix composites (Voyiadjis, G. Z., Ju, J. W., eds.), pp. 97–118. Amsterdam: Elsevier 1994.

    Google Scholar 

  13. Eringen, A. C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci.10, 425–435 (1972).

    Google Scholar 

  14. Eringen, A. C.: On nonlocal continuum thermodynamics. In: Modern developments in thermodynamics (Gal-Or, B., ed.). New York: Wiley 1974.

    Google Scholar 

  15. Eringen, A. C.: On nonlocal plasticity. Int. J. Eng. Sci.19, 1461–1474 (1981).

    Google Scholar 

  16. Aifantis, E. C.: On the microstructural origin of certain inelastic models. J. Eng. Mat. Tech.106, 326–330 (1984).

    Google Scholar 

  17. Aifantis, E. C.: The physics of plastic deformation. Int. J. Plasticity3, 211–247 (1987).

    Google Scholar 

  18. Dillon, O. W., Jr., Kratochvil, J.: A strain gradient theory of plasticity. Int. J. Solids Struct.6, 1513–1533 (1970).

    Google Scholar 

  19. Zbib, H. M., Aifantis, E. C.: On the localization and postlocalization behavior of plastic deformation. Part I: On the initiation of shear bands. Res. Mech.23, 261–277 (1988).

    Google Scholar 

  20. Zbib, H. T., Aifantis, E. C.: A gradient-dependent theory of plasticity: application to metal and soil instabilities. Appl. Mech. Rev.42, 295–304 (1989).

    Google Scholar 

  21. Zhu, H. T., Zbib, H. M.: A macroscopic model for plastic flow in metal-matrix composites. Int. J. Plasticity,II, 471–499 (1995).

    Google Scholar 

  22. Zbib, H. M., Aifantis, E. C.: On the gradient-dependent theory of plasticity and shear banding. Acta Mech.92, 209–225 (1992).

    Google Scholar 

  23. Zbib, H. M.: Size effect and shear banding in viscoplasticity with kinematic hardening. In: Material instabilities: theory and applications (Batra, R. C., Zbib, H. M.,eds.), pp. 19–33. AMD-Vol. 183/MD-Vol. 50 New York: ASME 1994.

    Google Scholar 

  24. Aifantis, E. C.: On the role of gradients in the localization of deformation and facture. Int. J. Eng. Sci.30, 1279–1299 (1990).

    Google Scholar 

  25. Aifantis, E. C.: Spatio-temporal instabilities in deformation and fracture. In: Computational material modeling (Noer, A., Needleman A., eds.), AD-Vol. 42/PVP-Vol. 294. New York: ASME 1994.

    Google Scholar 

  26. Muhlhaus, H. B., Aifantis, E. C.: A variational principle for gradient plasticity. Int. J. Solids Struct.28, 845–857 (1991).

    Google Scholar 

  27. Vardoulakis, I., Aifantis, E. C.: A gradient flow theory of plasticity for granular materials. Acta Mech.87, 197–217 (1991).

    Google Scholar 

  28. Zhu, H. T., Zbib, H. M., Khraisheh, M. K.: Flow strength and size effect of an Al−Si−Mg composite model system under multiaxial loadings. Scripta Metall. Mater.II, 1895–1902 (1995).

    Google Scholar 

  29. Aikin, R. M., Christodoulou, L.: The role of equiaxed particles on the yield stress of composites. Scripta Metall. Mater.25, 9–14 (1991).

    Google Scholar 

  30. Zhu, H. T., Zbib, H. M., Aifantis, E. C.: Flow strength and size effect in metal matrix composites. In: Micromechanics and constitutive modelling of composite materials (Zbib, H. M. et al., eds.), AMD-Vol. 202/MD-Vol. 61. New York: ASME (1995).

    Google Scholar 

  31. Ning, J., Aifantis, E. C.: Strain gradients and size effects in composites. In: Micromechanics and constitutive modelling of composite materials (Zbib, H. M. et al., eds.), AMD-Vol. 202/MD-Vol. 61. New York: ASME (1995).

    Google Scholar 

  32. Aifantis, E. C.: Higher order gradients and size effects. In: Size-scale effects in the failure mechanics of materials and structures, (Carbinteri, A., ed.), pp. 231–242. New York: Chapman and Hall 1995.

    Google Scholar 

  33. Aifantis, E. C.: Pattern formation in plasticity. Int. J. Eng. Sci.33, 2161–2178 (1995).

    Google Scholar 

Download references

Author information

Author notes

  1. H. T. Zhu & H. M. Zbib

    Present address: School of Mechanical and Materials Engineering, Washington State University, 99164-2920, Pullman, WA, USA

  2. E. C. Aifantis

    Present address: Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 49931, Houghton, MI, USA

Authors and Affiliations

    Authors
    1. H. T. Zhu
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. H. M. Zbib
      View author publications

      You can also search for this author in PubMed Google Scholar

    3. E. C. Aifantis
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Zhu, H.T., Zbib, H.M. & Aifantis, E.C. Strain gradients and continuum modeling of size effect in metal matrix composites. Acta Mechanica 121, 165–176 (1997). https://doi.org/10.1007/BF01262530

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01262530

    Keywords

    Search

    Navigation