Skip to main content
SpringerLink
Log in

Effect of a Third Invariant on the Properties and Structure of Constitutive Relationships for Powder Materials

  • Published:
Powder Metallurgy and Metal Ceramics Aims and scope

Abstract

The bahavior of powder materials is considered whose properties are sensitive to a third invariants of stress and strain rate. Nonlinear relationships between stress and strain rate tensors for isotropic compactable material are found. Limitations on the material parameters of the model that provide correct determination are formulated. Estimates of axial and radial stress during compaction with a rotating die are presented within the model developed. It is established that three-invariant models describe more accurately the reduction in operating parameters with an increase in rotation rate than models containing the first two variants.

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. A. Freidental and H. Geiringer, Mathematical Theories of an Inelastic Solid [Russian translation], Fizmatgiz, Moscow (1962).

    Google Scholar 

  2. A. Sawchuk and P. Stutz, “On formulation of stress-strain relations for soils at failure,” Angew. Math. Phys., 19, No. 5, 770–778 (1968).

    Google Scholar 

  3. M. B. Shtern, “Constitutive equations for plastic porous bodies, ” Poroshk. Metall., No. 4, 17–21 (1981).

    Google Scholar 

  4. E. Pavier and P. Doremus, “Triaxial characterization of iron powder behavior, ” Powder Met., 42, No. 4, 345–352 (1999).

    Google Scholar 

  5. V. Z. Midukov and V. D. Rud', “Experimental verification of the basic hypotheses of plasticity theory for porous bodies, ” Poroshk. Metall., No. 1, 6–17 (1982).

    Google Scholar 

  6. I. C. Sinka, A. C. F. Cocks, and J. H. Tweed, “Constitutive data for powder compaction modelling, ” J. Eng. Mat. Techn., No. 1, 241–259 (1999).

    Google Scholar 

  7. A. L. Gurson, “Continuum theory for ductile rupture by void nucleation and growth. I. Yield criteria and flow rules for porous ductile media, ” Trans. ASME J. Eng. Mat. Techn., 2–15 (1977).

  8. M. B. Shtern, “On the constitutive potential for powders and porous bodies, ” in: Mechanics of Granular and Porous Bodies, N. A. Fleck and A. C. F. Cocks (eds.), Kluwer Academic Publ., Dordrecht (1997).

    Google Scholar 

  9. P. Mosbah, Jun Kojima, S. Shima, and H. Kotera, “Influence of the third invariant on powder behavior during compaction, ” Proc. Int. Workshop on Modelling of Metal Powder Forming Processes (Grenoble, 21–23 July, 1997), Grenoble (1997).

  10. V. Z. Midukov, Study of the Features of Plastic Deformation for Materials with Irreversible Volumetric Compressibility, PhD Thesis [in Russian], Tomsk (1975).

  11. M. B. Shtern and A. C. F. Cocks, “The structure of constitutive laws for the compaction of metal powders, ” in: Recent Developments in Computer Modelling of Powder Metallurgy Processes, IOS Press (2001).

Download references

Author information

Authors and Affiliations

  1. National Academy of Sciences of Ukraine, Institute for Problems of Materials Science, ul. Krzhizhanovskogo 3, Kiev, Ukraine, 03142

    Mikhail B. Shtern

Authors
  1. Mikhail B. Shtern
    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

Shtern, M.B. Effect of a Third Invariant on the Properties and Structure of Constitutive Relationships for Powder Materials. Powder Metallurgy and Metal Ceramics 42, 329–335 (2003). https://doi.org/10.1023/B:PMMC.0000004151.45288.60

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:PMMC.0000004151.45288.60

Search

Navigation