Skip to main content

On Strain Hardening Modeling in Associated and Non-Associated Orthotropic Plasticity

  • Conference paper
  • First Online:
NUMISHEET 2022

Part of the book series: The Minerals, Metals & Materials Series ((MMMS))

  • 990 Accesses

Abstract

In rate-independent associated plasticity, the flow surface in stress space is identical to the yield surface given by a yield stress function. Two distinct stress functions are however needed in non-associated plasticity to specify the yield surface and the flow surface separately. In this study, we explore the possibility of modeling strain hardening in metal plasticity by a new equivalent stress function that may be different from both yield and flow stress functions. As an initial effort, we consider all stress functions to be quadratic and orthotropic to describe either isotropic or differential strain hardening behaviors of rolled sheet metals under plane stress. The advantages and limitations of using an independent equivalent stress function for strain hardening modeling in sheet metal plasticity are discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hill R (1950) The mathematical theory of plasticity. Oxford University Press, London

    Google Scholar 

  2. Lubliner J (1990) Plastic theory. Macmillan, New York

    Google Scholar 

  3. Maugin GA (1992) The thermomechanics of plasticity and fracture. Cambridge University Press, Cambridge

    Book  Google Scholar 

  4. Hill R (1948) A theory of yielding and plastic flow of anisotropic metals. Proc Royal Soc 193A:281–297

    Google Scholar 

  5. Hill R (1990) Constitutive modeling of orthotropic plasticity in sheet metals. J Mech Phys Solids 38:403–417

    Article  Google Scholar 

  6. Gotoh M (1977) A theory of plastic anisotropy based on a yield function of fourth order (plane stress state). Int J Mech Sci 19:505–520

    Article  Google Scholar 

  7. Barlat F, Yoon JW, Cazacu O (2007) On linear transformations of stress tensors for the description of plastic anisotropy. Int J Plast 23:876–896

    Article  CAS  Google Scholar 

  8. Stoughton TS (2002) A non-associated flow rule for sheet metal forming. Int J Plast 18:687–714

    Article  Google Scholar 

  9. Tong W, Alharbi M (2017) Comparative evaluation of non-associated quadratic and associated quartic plasticity models for orthotropic sheet metals. Int J Solids Struct 128:133–48

    Article  Google Scholar 

  10. Cvitanic V, Vlak F, Lozina Z (2008) A finite element formulation based on non-associated plasticity for sheet metal forming. Int J Plast 24:646–687

    Article  CAS  Google Scholar 

  11. Stoughton TB, Yoon JW (2009) Anisotropic hardening and non-associated flow in proportional loading of sheet metals. Int J Plast 25:1777–1817

    Article  CAS  Google Scholar 

  12. Safaei M, Yoon JW, Waele WD (2014) Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation. Int J Plast 58:219–238

    Article  CAS  Google Scholar 

  13. Tong W (2005) A planar plastic flow theory of orthotropic sheets and the experimental procedure for its evaluations. Proc R Soc Lond A 461:1775–1809

    Google Scholar 

  14. Tong W (2006) A plane stress anisotropic plastic flow theory for orthotropic sheet metals. Int J Plast 22:497–535

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wei Tong .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Minerals, Metals & Materials Society

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sheng, J., Alharbi, M., Yang, SY., Tong, W. (2022). On Strain Hardening Modeling in Associated and Non-Associated Orthotropic Plasticity. In: Inal, K., Levesque, J., Worswick, M., Butcher, C. (eds) NUMISHEET 2022. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-031-06212-4_34

Download citation

Publish with us

Policies and ethics