Skip to main content
SpringerLink
Log in

Extension of Combined Self-Consistent and Mori-Tanaka Approach to Evaluation of Elastoplastic Property Of Particulate Composites

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evaluate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element (RVE) of a particulate composite, these inclusions are separated into two groups, with volume fractions (1 − λ−1)c and c/λ over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as λ = 1 and λ = ∞, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. Furthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced λ can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.

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. Hershey, A.V., The elasticity of an isotropic aggregate of anisotropic cubic crystals. Journal of Applied Mechanics, 1954, 21(3): 236–240.

    MATH  Google Scholar 

  2. Kröner, E., Berechung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls. Zeitschrift für Physik, 1958, 151(4): 504–518.

    Article  Google Scholar 

  3. Budiansky, B., On the elastic moduli of some heterogeneous materials. Journal of the Mechanics and Physics of Solids, 1965, 13(4): 223–227.

    Article  Google Scholar 

  4. Hill, R., A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids, 1965, 13(4): 213–222.

    Article  Google Scholar 

  5. Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 1973, 21(5): 571–574.

    Article  Google Scholar 

  6. Nemat-Nasser, S. and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland: Elsevier, 1993.

    MATH  Google Scholar 

  7. Hori, M. and Nemat-Nasser, S., Double-inclusion model and overall moduli of multi-phase composites. Mechanics of Materials, 1993, 14(3): 189–206.

    Article  Google Scholar 

  8. Christensen, R.M. and Lo, K.H., Solutions for effective shear properties in three phase space and cylinder model. Journal of the Mechanics and Physics of Solids, 1979, 27(4): 315–330.

    Article  Google Scholar 

  9. Huang, Y., Hu, K.X. and Chandra, A., A generalized self-consistent mechanics method for microcracked solids. Journal of the Mechanics and Physics of Solids, 1994, 42(8): 1273–1291.

    Article  Google Scholar 

  10. Huang, Y., Hu, K.X., Wei, X. and Chandra, A., A generalized self-consistent mechanics method for a composite with multi-phase inclusions. Journal of the Mechanics and Physics of Solids, 1994, 42(3): 491–504.

    Article  Google Scholar 

  11. Hu, G.K. and Weng, G.J., Some reflections on the Mori-Tanaka and Ponte Castañeda-Willis methods with randomly oriented ellipsoidal inclusions. Acta Mechanica, 2000, 140: 31–40.

    Article  Google Scholar 

  12. Li, L.X. and Wang, T.J., A unified approach to predict overall properties of composite materials. Materials Characterization, 2005, 54(1): 49–62.

    Article  Google Scholar 

  13. Kröner, E., Zur plastischen verformung des vielkristalls. Acta Metallurgica, 1961, 9(2): 155–161.

    Article  Google Scholar 

  14. Hill, R., Continuum micro-mechanisms of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids, 1965, 13(2): 89–101.

    Article  Google Scholar 

  15. Hutchinson, J.W., Bounds and self-consistent estimates for creep of polycrystalline materials. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 1976, 348(1652): 101–127.

    Article  Google Scholar 

  16. Pindera, M.J. and Aboudi, J., Micromechanical analysis of yielding of metal matrix composites. International Journal of Plasticity, 1988, 4(3): 195–214.

    Article  Google Scholar 

  17. Berveiller, M. and Zaoui, A., An extension of the self-consistent scheme to plastically flowing polycrystals. Journal of the Mechanics and Physics of Solids, 1979, 26(4): 325–344.

    MATH  Google Scholar 

  18. Molinari, A., Canova, G.R. and Ahzi, S., A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metallurgica, 1987, 35(12): 2983–2994.

    Article  Google Scholar 

  19. Lebensohn, R. and Tome, C., A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metallurgica et Materialia, 1993, 41(9): 2611–2624.

    Article  Google Scholar 

  20. Fotiu, P.A. and Memat-Nassar, S., Overall properties of elastic-viscoplastic periotic composites. International Journal of Plasticity, 1996, 12(2): 163–190.

    Article  Google Scholar 

  21. Mercier, S. and Molinari, A., Homogenization of elastic-viscoplastic heterogeneous materials: self-consistent and Mori-Tanaka schemes. International Journal of Plasticity, 2009, 25(6): 1024–1048.

    Article  Google Scholar 

  22. Zhang, M., Chen, J., Zhu, J. and Chen, J., Experimental evaluation on modulus of equivalent homogeneous ettringite. Acta Mechanica Solida Sinica, 2009, 22(4): 320–327.

    Article  Google Scholar 

  23. Deng, F. and Zheng, Q., Interaction models for effective thermal and electric conductivities of carbon nanotube composites. Acta Mechanica Solida Sinica, 2009, 22(1): 1–17.

    Article  Google Scholar 

  24. Christensen, R.M., A critical evaluation for a class of micro-mechanical models. Journal of the Mechanics and Physics of Solids, 1990, 38(3): 379–404.

    Article  Google Scholar 

  25. Huang, Y., Kwang, K.C., Hu, K.X. and Chandra, A., A unified energy approach to a class of micromechanics models for composite materials. Acta Mechanica Sinica, 1995, 11(1): 59–75.

    Article  Google Scholar 

  26. Peng, X., Hu, N., Zheng, H. and Fukunaga, H., Evaluation of mechanical properties of particulate composites with a self-consistent and Mori-Tanaka approach. Mechanics of Materials, 2009, 41(12): 1288–1297.

    Article  Google Scholar 

  27. Benveniste, Y., A new approach to the application of Mori-Tanaka’s theory in composite materials. Mechanics of Materials, 1987, 6(2): 147–157.

    Article  Google Scholar 

  28. Fan, J. and Peng, X., A physically based constitutive description for nonproportional cyclic plasticity. Journal of Engineering Materials and Technology, 1991, 113(2): 254–262.

    Article  Google Scholar 

  29. Peng, X. and Fan, J., A numerical approach for nonclassical plasticity, computers and structures. Computers & Structures, 1993, 47(2): 313–320.

    Article  Google Scholar 

  30. Peng, X., Long, X. and Fan, J., Micro-macro description for elastoplasticity of materials with lamellar microstructure using anisotropic Eshelby tensor. Mechanics of Advanced Materials and Structures, 2009, 16(7): 542–551.

    Article  Google Scholar 

  31. Kouzeli, M. and Dunand, D.C., Effect of reinforcement connectivity on the elasto-plastic behavior of aluminum composites containing sub-micron alumina particles. Acta Materialia, 2003, 51(20): 6105–6121.

    Article  Google Scholar 

  32. Lloyd, D.J., Particle-reinforced aluminumand magnesiummatrix composite. International Materials Reviews, 1994, 39(1): 1–23.

    Article  Google Scholar 

  33. Derrien, K., Baptiste, D., Guedra-Degeorges, D. and Foulquier, J., Multiscale modeling of the damaged plastic behavior and failure of Al/SiCp composites. International Journal of Plasticity, 1999, 15(6): 667–685.

    Article  Google Scholar 

  34. Nakamura, Y., Yamaguchi, M., Okubo, M. and Matsumoto, T., Effects of particle size on mechanical and impact properties of epoxy resin filled with spherical silica. Jourmal of the applied polymer Science, 1992, 45(7): 1281–1289.

    Article  Google Scholar 

  35. Barai, P. and Weng, G.J., The competition of grain size and porosity in the viscoplastic response of nanocrystalline solids. International Journal of Plasticity, 2008, 24(8): 1380–1410.

    Article  Google Scholar 

  36. Marcadon, V., Herve, E. and Zaoui, A., Micromechanical modeling of packing and size effects in particulate composites. International Journal of Solids and Structures, 2007, 44(25–26): 8213–8228.

    Article  Google Scholar 

  37. Ortiz, M. and Molinari, A., Microstructural thermal stresses in ceramic materials. Journal of the Mechanics and Physics of Solids, 1988, 36(4): 385–400.

    Article  Google Scholar 

  38. Kreher, W., Molinari, A., Residual stresses in polycrystals as influenced by grain shape and texture. Journal of the Mechanics and Physics of Solids, 1993, 41(12): 1955–1977.

    Article  Google Scholar 

  39. Ponte-Castañeda, P., Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I theory. Journal of the Mechanics and Physics of Solids, 2002, 50(4): 737–757.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, China

    Xianghe Peng, Ning Hu, Xuesong Long & Hengwei Zheng

  2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Xianghe Peng, Ning Hu, Xuesong Long & Hengwei Zheng

  3. Department of Mechanical Engineering, Chiba University, 1-33 Yayoi, Inage-ku, Chiba, 263-8522, Japan

    Ning Hu

Authors
  1. Xianghe Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ning Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuesong Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hengwei Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianghe Peng.

Additional information

Project supported by the National Natural Science Foundation of China — NSAF (No. 10976032) and Japan Society for the Promotion of Science (No. L08538).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, X., Hu, N., Long, X. et al. Extension of Combined Self-Consistent and Mori-Tanaka Approach to Evaluation of Elastoplastic Property Of Particulate Composites. Acta Mech. Solida Sin. 26, 71–82 (2013). https://doi.org/10.1016/S0894-9166(13)60008-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(13)60008-7

Key words

Search

Navigation