Skip to main content
SpringerLink
Log in

Anisotropic Plasticity and Application to Plane Stress

  • Living reference work entry
  • First Online:
Encyclopedia of Continuum Mechanics

Synonyms

Plane stress description of plastic anisotropy

Definitions

Plasticity is the ability of a material to deform in an irreversible manner. Unlike elasticity for which deformations are reversible, plasticity leads to permanent shape changes after a sufficient load is applied to a material. Anisotropic plasticity is the dependence of plastic properties on the loading direction. For plane stress states, loading is defined using only three stress components out of six for a general stress tensor. The description of plastic anisotropy for plane stress states is simpler than for general stress states but it has a wide range of practical applications in processes such as sheet forming.

Introduction

In uniaxial tension, the stress-strain behavior of metals and alloys at low strain is, at first order, reversible and linear. This behavior is well described by Hooke’s law, in which the stress is proportional to the strain through the elastic modulus E. This law can be generalized to all...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • An YG, Vegter H, Elliott L (2004) A novel and simple method for the measurement of plane strain work hardening. J Mater Process Technol 155–156: 1616–1622

    Article  Google Scholar 

  • Aretz H (2004) Applications of a new plane stress yield function to orthotropic steel and aluminium sheet metals. Model Simul Mater Sci Eng 12:491–509

    Article  Google Scholar 

  • Aretz H, Barlat F (2013) New convex yield functions for orthotropic metal plasticity. Int J Non-Linear Mech 51:97–111

    Article  Google Scholar 

  • Banabic D, Aretz H, Comsa DS, Paraianu L (2005) An improved analytical description of orthotropy in metallic sheets. Int J Plast 21:493–512

    Article  MATH  Google Scholar 

  • Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7:693–712

    Article  Google Scholar 

  • Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003a) Plane stress yield function for aluminum alloy sheets–Part I: theory. Int J Plast 19:1297–1319

    Article  MATH  Google Scholar 

  • Barlat F, Ferreira Duarte JM, Gracio JJ, Lopes AB, Rauch EF (2003b) Plastic flow for non-monotonic loading conditions of an aluminum alloy sheet sample. Int J Plast 19:1215–1244

    Article  MATH  Google Scholar 

  • Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transformation-based anisotropic yield functions. Int J Plast 21:1009–1039

    Article  MATH  Google Scholar 

  • 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  MATH  Google Scholar 

  • Bron, F, Besson, J (2005) A yield function for anisotropic materials. Application to aluminum alloys. Int J Plast 20:937–963.

    Article  MATH  Google Scholar 

  • Cazacu O, Barlat F (2004) A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals. Int J Plast 20:2027–2045

    Article  MATH  Google Scholar 

  • Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal close packed metals. Int J Plast 22:1171–1194

    Article  MATH  Google Scholar 

  • Coppieters S, Lava P, Sol H, Van Bael A, Van Houtte P, Debruyne D (2010) Determination of the flow stress and contact friction of sheet metal in a multi-layered upsetting test. J Mater Proc Technol 210:1290–1296

    Article  Google Scholar 

  • Deng N, Kuwabara T, Korkolis YP (2015) Cruciform specimen design and verification for constitutive identification of anisotropic sheets. Exp Mech 55:1005–1022

    Article  Google Scholar 

  • Dick CP, Korkolis YP (2015) Anisotropy of thin-walled tubes by a new method of combined tension and shear loading. Int J Plast 71:87–112

    Article  Google Scholar 

  • Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. J Appl Mech 16:349–357

    MathSciNet  MATH  Google Scholar 

  • Hakoyama T, Kuwabara T (2015) Effect of biaxial work hardening modeling for sheet metals on the accuracy of forming limit analyses using the Marciniak-Kuczynski approach. In: Altenbach H, Matsuda T, Okumura D (eds) From creep damage mechanics to homogenization methods. Springer, Cham, pp 67–95

    Chapter  Google Scholar 

  • Hanabusa Y, Takizawa H, Kuwabara T (2010) Evaluation of accuracy of stress measurements determined in biaxial stress tests with cruciform specimen using numerical method. Steel Res Int 81:1376–1379

    Google Scholar 

  • Hanabusa Y, Takizawa H, Kuwabara T (2013) Numerical verification of a biaxial tensile test method using a cruciform specimen. J Mater Process Technol 213:961–970

    Article  Google Scholar 

  • Hannon A, Tiernan P (2008) A review of planar biaxial tensile test systems for sheet metal. J Mater Process Technol 198:1–13

    Article  Google Scholar 

  • Hecker SS (1976) Experimental studies of yield phenomena in biaxially loaded metals. In: Stricklin JA, Saczalski KH (eds) Constitutive equations in viscoplasticity: computational and engineering aspects. ASME, New York, pp 1–33

    Google Scholar 

  • Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face centred cubic crystals. J Appl Mech 21:241–249

    MATH  Google Scholar 

  • Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A193:281–297

    Article  MathSciNet  MATH  Google Scholar 

  • Hill R, Hecker SS, Stout MG (1994) An investigation of plastic flow and differential work hardening in orthotropic brass tubes under fluid pressure and axial load. Int J Solids Struct 21:2999–3021

    Article  MATH  Google Scholar 

  • Ikegami K (1979) Experimental plasticity on the anisotropy of metals. In: Boehler JP (ed) Mechanical behavior of anisotropic solids. Proceedings of the Euromech Colloquim 115 Colloques Inter, du CNRS Paris, pp 201–242

    Google Scholar 

  • ISO 10113 (2006) Metallic materials—sheet and strip—determination of plastic strain ratio

    Google Scholar 

  • ISO 10275 (2007) Metallic materials—sheet and strip—determination of tensile strain hardening exponent

    Google Scholar 

  • ISO 6892-1 (2009) Metallic materials—tensile testing—Part 1: Method of test at room temperature

    Google Scholar 

  • ISO 16808 (2014a) Metallic materials—sheet and strip—determination of biaxial stress-strain curve by means of bulge test with optical measuring systems

    Google Scholar 

  • ISO 16842 (2014b) Metallic materials −Sheet and strip −Biaxial tensile testing method using a cruciform test piece

    Google Scholar 

  • Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859–1886

    Article  MATH  Google Scholar 

  • Korkolis YP, Kyriakides S (2008) Inflation and burst of anisotropic aluminum tubes for hydroforming applications. Int J Plast 24:509–543

    Article  MATH  Google Scholar 

  • Kuwabara T (2007) Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations. Int J Plast 23:385–419

    Article  MATH  Google Scholar 

  • Kuwabara T, Sugawara F (2013) Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range. Int J Plast 45:103–118

    Article  Google Scholar 

  • Kuwabara T, Yoshida K, Narihara K, Takahashi S (2005) Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure. Int J Plast 21:101–117

    Article  MATH  Google Scholar 

  • Kuwabara T, Horiuchi Y, Uema N, Ziegelheimova J (2007) Material testing method of applying in-plane combined tension-compression stresses to sheet specimen. J JSTP 48:630–634 (in Japanese)

    Article  Google Scholar 

  • Kuwabara T, Kumano Y, Ziegelheim J, Kurosaki I (2009) Tension-compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior. Int J Plast 25:1759–1776

    Article  MATH  Google Scholar 

  • Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming pencil glide. Int J Mech Sci 22:419–430

    Article  Google Scholar 

  • Lowden MAW, Hutchinson WB (1975) Texture strengthening and strength differential in titanium-6A-4V. Metall Trans 6A:441–448

    Article  Google Scholar 

  • Michno MJ Jr, Findley WN (1976) An historical perspective of yield surface investigations for metals. Int J Non-Linear Mech 11:59–82

    Article  MATH  Google Scholar 

  • Mohr D, Oswald M (2008) A new experimental technique for the multi-axial testing of advanced high strength steel sheets. Exp Mech 48:65–77

    Article  Google Scholar 

  • Mulder J, Vegter H, Aretz H, Keller S, Van den Boogaard AH (2015) Accurate determination of flow curves using the bulge test with optical measuring systems. J Mater Process Technol 226:169–187

    Article  Google Scholar 

  • Noma N, Kuwabara T (2012) Specimen geometry optimization for in-plane reverse loading test of sheet metal and experimental validation. Steel Res Int, Special Edition: 14th Metal Forming:1283–1286

    Google Scholar 

  • Phillips A (1986) A review of quasistatic experimental plasticity and viscoplasticity. Int J Plast 2:315–328

    Article  Google Scholar 

  • Ranta-Eskola AJ (1979) Use of the hydraulic bulge test in biaxial tensile testing. Int J Mech Sci 21:457–465

    Article  Google Scholar 

  • Ripley PW, Korkolis YP (2016) Multiaxial deformation apparatus for testing of microtubes under combined axial-force and internal-pressure. Exp Mech 56:273–286

    Article  Google Scholar 

  • Skrzypek JJ, Ganczarski AW (2015) Mechanics of anisotropic materials. Springer, London

    Book  MATH  Google Scholar 

  • Spitzig WA, Richmond O (1984) The effect of pressure on the flow stress of metals. Acta Metall 32:457–463

    Article  Google Scholar 

  • Spitzig WA, Sober RJ, Richmond O (1975) Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall 23:885–893

    Article  Google Scholar 

  • Tardif N, Kyriakides S (2012) Determination of anisotropy and material hardening for aluminum sheet metal. Int J Solids Struct 49:3496–3506

    Article  Google Scholar 

  • Tian H, Brownell B, Baral M, Korkolis YP (2017) Earing in cup-drawing of anisotropic Al-6022-T4 sheets. Int J Mater Form 10:329–343

    Article  Google Scholar 

  • Tozawa Y (1978) Plastic deformation behavior under conditions of combined stress. In: Koistinen DP, Wang NM (eds) Mechanics of sheet metal forming. Plenum Press, New York, pp 81–110

    Chapter  Google Scholar 

  • van den Boogaard AH, Havinga J, Belin A, Barlat F (2016) Parameter reduction for the Yld2004-18p yield criterion. Int J Mater Form 9:175–178

    Article  Google Scholar 

  • Vegter H, van den Boogaard AH (2006) A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. Int J Plast 22:557–580

    Article  MATH  Google Scholar 

  • von Mises R (1928) Mechanics der plastischen Formänderung von Kristallen. Zeitschrift Angewandte Mathematik Mechanik 8:161–185

    Article  MATH  Google Scholar 

  • Yapici GG, Beyerlein IJ, Karaman I, Tome CN (2007) Tension-compression asymmetry in severely deformed pure copper. Acta Mater 55:4603–4613

    Article  Google Scholar 

  • Yoshida K (2013) Evaluation of stress and strain measurement accuracy in hydraulic bulge test with the aid of finite-element analysis. ISIJ Int 53:86–95

    Article  Google Scholar 

  • Yu MH (2002) Advances in strength theories for materials under complex stress state in the 20th century. Appl Mech Rev 55:198–218

    Article  Google Scholar 

  • Życzkowski M (1981) Combined loadings in the theory of plasticity. Polish Scientific Publisher, Warsaw

    MATH  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the supports of POSCO and the Global Innovation Research Organization in TUAT for this entry. In addition, the authors are indebted to Dr. Tomoyuki Hakoyama (The RIKEN) for help with the parameter identification analysis in section “Application to Steel”.

Author information

Authors and Affiliations

  1. Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang, Republic of Korea

    Frédéric Barlat

  2. Division of Advanced Mechanical Systems Engineering, Institute of Engineering (double as Institute of Global Innovation Research), Tokyo University of Agriculture and Technology, Tokyo, Japan

    Toshihiko Kuwabara

  3. Department of Mechanical Engineering, University of New Hampshire, Durham, NH, USA

    Yannis P. Korkolis

Authors
  1. Frédéric Barlat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Toshihiko Kuwabara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yannis P. Korkolis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frédéric Barlat .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, 119526, Moscow, Russia

    Sergey Alexandrov

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Barlat, F., Kuwabara, T., Korkolis, Y.P. (2018). Anisotropic Plasticity and Application to Plane Stress. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_225-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_225-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation