Skip to main content
SpringerLink
Log in

Determination of the ultimate plastic capacity for powder materials based on the plastic flow model for porous solids. I. Criterion for exhaustion of the ultimate plastic capacity

  • Theory and Technology of the Process of Forming Articles
  • Published:
Powder Metallurgy and Metal Ceramics Aims and scope

Abstract

This paper is devoted to the theoretical definition of the ultimate plastic capacity for porous solids. The model is based on the assumption that ductile fracture is defined by loss of physical stability. Porosity, strain in hard phase, and decohesion are taken into account as internal variables. We suggest a method for defining the limit surface on the basis of the constitutive relations of plasticity theory for a porous solid.

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. Yu. G. Dorofeev and V. V. Sinel’shchikov, “Characteristics of deformation and crack formation in heated porous semifabricates,”Poroshk. Metall., No. 1, 25–29 (1980).

    Google Scholar 

  2. Ya. E. Beigel’zimer, B. M. Éfros, V. N. Varyukhin, and A. V. Spuskanyuk, “Physical mechanics of processes of deformation and failure of materials under high pressure conditions,” in:Physics of Strength and Plasticity of Materials: Abstracts, Fourteenth International Conference (Samara, 27–30 June, 1995) [in Russian], Samara (1995), pp. 25–26.

  3. A. V. Stepanenko, L. A. Isaevich, and V. E. Kharlan,Pressure Working of Powder Media [in Russian], Navuka i Tekhnika, Minsk (1993).

    Google Scholar 

  4. Yu. N. Podrezov, A. Yu. Koval’, and D. G. Verbilo,Preprint, Ukraine National Academy of Sciences, Institute for Problems of Materials Science; 98–7, Kiev (1998).

  5. J. J. Burke and V. Weiss (eds.),Powder Metallurgy for High-Performance Applications [Russian translation], Metallurgiya, Moscow (1977).

    Google Scholar 

  6. M. Oyane, S. Sima, and T. Tabata, “Consideration of basic equations and their application in the forming of metal powder and porous metals,”J. Mech. Work. Technol.,1, 325–341 (1978).

    Article  CAS  Google Scholar 

  7. A. A. Notych and E. V. Zvonarev, “Methods for evaluation of technological plasticity in pressure working of powdered metals. II. Failure criteria taking into account the stress state”,Poroshk. Metall., No. 9, 10–14 (1991).

    Google Scholar 

  8. G. A. Smirnov-Alyaev,Mechanical Principles of Plastic Working of Metals [in Russian], Mashinostroenie, Moscow/Leningrad (1968).

    Google Scholar 

  9. V. L. Kolmogorov,Stresses, Strains, and Failure [in Russian], Metallurgiya, Moscow (1970).

    Google Scholar 

  10. G. S. Pisarenko and A. A. Lebedev,Deformation and Strength of Materials for a Complex Stress State [in Russian], Nauk, Dumka, Kiev (1976).

    Google Scholar 

  11. V. A. Ogorodnikov,Assessment of Deformability of Metals in Pressure Working [in Russian], Vishcha Shk., Kiev (1983).

    Google Scholar 

  12. E. P. Unksov and A. G. Ovchinnikov (general ed.),Theory of Forging and Stamping: Textbook [in Russian], Mashinostroenie, Moscow (1992).

    Google Scholar 

  13. L. M. Kachanov,Principles of Fracture Mechanics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  14. N. A. Fleck, J. W. Hutchinson, and V. Tvergaard, “Softening by void nucleation and growth in tension and shear,”J. Mech. Phys. Sol.,37, No. 4, 515–540 (1989).

    Article  Google Scholar 

  15. V. Tvergaard, “Material failure by void growth to coalescence,” in:Advances in Applied Mechanics, J. W. Hutchinson and T. Y. Wu (eds.), Academic Press, New York (1990), Vol. 27, pp. 83–151.

    Google Scholar 

  16. A. B. Richelsen and V. Tvergaard, Dilatant Plasticity or Upper Bound Estimates for Porous Ductile Solids, The Danish Center for Applied Mathematics and Mechanics, Lingby (1993),Report N 464, July.

    Google Scholar 

  17. R. J. Green, “A plastic theory for porous solid,”Int. J. Mech. Sci.,14, 215–224 (1972).

    Article  Google Scholar 

  18. S. Shima and M. Oyane, “Plasticity theory for porous metals,”Int. J. Mech. Sci.,18, 16–23 (1976).

    Article  Google Scholar 

  19. I. F. Martynova and M. B. Shtern, “Plasticity equation for a porous solid, taking into account the true strains of th base material,”Poroshk. Metall., No. 1, 23–29 (1978).

    Google Scholar 

  20. M. Abouaf and J. L. Chenot, “Numerical simulation of hot working of metal powders,”J. Mech. Theor. Appl.,5, 121 (1986).

    Google Scholar 

  21. G. L. Petrosyan, “Plasticity theory for porous solids,”Izv. Vuzov. Mashinostroenie, No. 5, 10–13 (1977).

    Google Scholar 

  22. A. M. Laptev,Izv. Vuzov. Mashinostroenie, No. 4, 153–156 (1978).

    Google Scholar 

  23. M. B. Shtern, “Model for deformation processes in compressible materials taking into account pore formation. I. Constitutive equations and the loading surface,”Poroshk. Metall., No. 5, 28–34 (1989).

    Google Scholar 

  24. M. B. Shtern, “Model of deformation processes in compressible materials taking into account pore formation. II. Uniaxial tension and compression of porous solids,”Poroshk. Metall., No. 6, 34–39 (1989).

    Google Scholar 

  25. E. Pavier and P. Doremus, “Comparison between constitutive equation modeling the compaction of iron powder and experimental data obtained with trial tests,” in:International Workshop on Modeling of Metal Powder Forming Processes (Grenoble, France, 21–23 July 1997), Grenoble (1997), pp. 1–8.

  26. S. Shima, H. Kotera, P. Mosbah, and J. Kojima, “A study of mechanical behavior of iron powders,” in:International Workshop on Modeling of Metal Powder Forming Processes (Grenoble, France, 21–23 July 1997), Grenoble (1997), pp. 9–10.

  27. J. Brandt and P. Lindskog, “A constitutive model for compaction of granular media with account for deformation induced anisotropy,” in:International Workshop on Modeling of Metal Powder Forming Processes (Grenoble, France, 21–23 July 1997), Grenoble (1997), pp. 41–56.

  28. H. Ziegler,Extremal Principles of the Thermodynamics of Irreversible Processes and Mechanics of Continuous Media [author and title not verified], [Russian translation], Moscow (1966).

  29. P. Germain,Course in Continuum Mechanics [Russian translation from French], Vyssh. Shk., Moscow (1983).

    Google Scholar 

  30. M. B. Shtern, “Development of a theory for pressing powders and a theory for the plasticity of porous solids,”Poroshk. Metall., No. 9, 12–24 (1992).

    Google Scholar 

  31. A. Cocks, “Inelastic deformation of porous materials,”J. Mech. Phys. Sol.,37, No. 6, 693–715 (1989).

    Article  Google Scholar 

  32. M. B. Shtern, “On the constitutive potentials for porous bodies and powders,” in:Mechanics of Granular and Porous Materials, Fleck and Cocks (eds.), (1997).

  33. V. V. Skorokhod,Rheological Principles of Sintering Theory [in Russian], Nauk. Dumka, Kiev (1972).

    Google Scholar 

  34. V. P. Katashinskii, “Localization of deformation during compaction of powders in an open volume,” in:Rheological Models and Deformation Processes in Porous Powdered and Composite Materials [in Russian], Nauk, Dumka, Kiev (1985), pp. 145–152.

    Google Scholar 

  35. P. V. Lade, “Elasto-plastic stress-strain theory for cohesionless soil with curved yield surface,”Int. J. Sol. Struct.,13, 1019–1035 (1977).

    Article  Google Scholar 

  36. V. N. Nikolaevsky,Mechanics of Porous and Fractured Media, World Scientific, Singapore (1990).

    Google Scholar 

  37. V. Tvergaard, “Effect of yield surface curvature and void nucleation on plastic flow localization,”J. Mech. Phys. Sol. 35, No. 1, 43–91 (1987).

    Article  Google Scholar 

Download references

Authors
  1. M. B. Shtern
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Dudunov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute for Problems of Materials Science, Ukraine National Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 11–12(410), pp. 31–40, November–December, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shtern, M.B., Dudunov, V.D. Determination of the ultimate plastic capacity for powder materials based on the plastic flow model for porous solids. I. Criterion for exhaustion of the ultimate plastic capacity. Powder Metall Met Ceram 38, 560–568 (1999). https://doi.org/10.1007/BF02676187

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02676187

Keywords

Search

Navigation