Skip to main content

Anisotropy of Yield/Failure Criteria—Comparison of Explicit and Implicit Formulations

  • 253 Accesses

Part of the CISM International Centre for Mechanical Sciences book series (CISM,volume 605)

Abstract

Six lectures on anisotropic plasticity comprise the following subjects: description of anisotropy influence on limit criteria (yield/failure) for modern homogeneous metallic alloys, anisotropy of limit criteria, critical comparison of explicit versus implicit approaches, discussion on of physical interpretation and convexity of implicit approach.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-031-04354-3_3
  • Chapter length: 55 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   129.00
Price excludes VAT (USA)
  • ISBN: 978-3-031-04354-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   169.99
Price excludes VAT (USA)
Fig. 3.1
Fig. 3.2
Fig. 3.3
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 3.8
Fig. 3.9
Fig. 3.10
Fig. 3.11
Fig. 3.12
Fig. 3.13
Fig. 3.14
Fig. 3.15

References

  • Barlat, F., Brem, J. C., Yoon, J. W., Chung, K., Dick, R. E., Lege, D. J., et al. (2003). Plane stress function for aluminium alloy sheets—Part I: Theory. International Journal of Plasticity, 19, 1297–1319.

    CrossRef  MATH  Google Scholar 

  • Betten, J. (1988). Applications of tensor functions to the formulation of yield criteria for anisotropic materials. International Journal of Plasticity, 4, 29–46.

    CrossRef  MATH  Google Scholar 

  • Boehler, J. P., & Sawczuk, A. (1970). Equilibre limite des sols anisotropes. J. Mécanique, 9, 5–33.

    MATH  Google Scholar 

  • Cazacu, O., & Barlat, F. (2004). A criterion for description of anisotropy and yield differential effects in pressure-insensitive materials. International Journal of Plasticity, 20, 2027–2045.

    CrossRef  MATH  Google Scholar 

  • Cazacu, O., Planckett, B., & Barlat, F. (2006). Orthotropic yield criterion for hexagonal close packed metals. International Journal of Plastics, 22, 1171–1194.

    CrossRef  MATH  Google Scholar 

  • Chen, W. F., & Han, D. J. (1995). Plasticity for Structural Engineers. Berlin, Heidelberg: Springer.

    MATH  Google Scholar 

  • Dunand, M., Maertens, A. P., Luo, M., & Mohr, D. (2012). Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading—Part I: Plasticity. International Journal of Plasticity, 36, 34–49.

    CrossRef  Google Scholar 

  • Ganczarski, A., & Lenczowski, J. (1997). On the convexity of the Goldenblatt-Kopnov yield condition. Archives of Mechanics, 49(3), 461–475.

    MathSciNet  MATH  Google Scholar 

  • Ganczarski, A., & Skrzypek, J. (2009). Plasticity of Engineering Materials (in Polish), Issue of Cracow University Technology.

    Google Scholar 

  • Ganczarski, A., & Skrzypek, J. (2011). Modeling of limit surfaces for transversely isotropic composite SCS-6/Ti-15-3 (in Polish). Acta Mechanica et Automatica, 5(3), 24–30.

    Google Scholar 

  • Ganczarski, A., & Skrzypek, J. (2013). Mechanics of Novel Materials (in Polish). Wyd. Politechniki Krakowskie

    Google Scholar 

  • Ganczarski, A., & Skrzypek, J. (2014). Constraints on the applicability range of Hill’s criterion: Strong orthotropy or transverse isotropy. Acta Mechanica, 225, 2568–2582.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Ganczarski, A., & Adamski, M. (2015). Tetragonal or hexagonal symmetry in modeling of yield criteria for transversely isotropic materials. Acta Mechanica et Automatica, 29, 125–128.

    Google Scholar 

  • Goldenblat, I. I. (1995). Some Problems of Mechanics of Deformable Media. Moskva: Gostekhizdat (in Russian).

    Google Scholar 

  • И.И. Гольденблат, В.А. Копнов, Обобщенная теория пластического течения анизотропных сред, Сборник Строительная Механика, СтроЙиздат, Москва, pages 307–319, 1966.

    Google Scholar 

  • Haigh, B. F. (1920). The strain-energy function and the elastic limit. Engineering, London, 109, 158–160.

    Google Scholar 

  • Herakovich, C. T., & Aboudi, J. (1999). Thermal effects in composites. In Thermal Stresses V (pp. 1–142). Lastran Corp. Publ. Division.

    Google Scholar 

  • Hill, R. (1948). A theory of the yielding and plastic flow of anisotropic metals. Proceedings of The Royal Society London, A193, 281–297.

    MathSciNet  MATH  Google Scholar 

  • Hill, R. (1950). The Mathematical Theory of Plasticity. Oxford: Clarendon Press.

    MATH  Google Scholar 

  • Hosford, W. F., & Backhofen, W. A. (1964). Strength and plasticity of textured metals. In Fundamentals of Deformation Processing (pp. 259–298). Syracuse University Press.

    Google Scholar 

  • Hosford, W. F. (1972). A generalized isotropic yield criterion. Transactions of the ASME, E39(2), 607–609.

    CrossRef  Google Scholar 

  • Hu, Z. W., & Marin, J. (1956). Anisotropic loading functions for combined stresses in the plastic range. The Journal of Applied Mechanics, 22, 1.

    Google Scholar 

  • Jackson, L. R., Smith, K. F., & Lankford, W. T. (1948). Plastic flow in anisotropic steel sheet. American Institute of Mining and Metallurgical Engineers, 2440, 1–15.

    Google Scholar 

  • Khan, A. S., Kazmi, R., & Farrokh, B. (2007). Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti-6Al-4V titanium alloy over wide ranges of strain rates and temperatures. International Journal of Plasticity, 23, 931–950.

    CrossRef  MATH  Google Scholar 

  • Khan, A. S., & Liu, H. (2012). Strain rate and temperature dependent fracture criteria for isotropic and anisotropic metals. International Journal of Plasticity, 37, 1–15.

    CrossRef  Google Scholar 

  • Khan, A. S., Yu, S., & Liu, H. (2012). Deformation enhanced anisotropic responses of Ti-6Al-4V alloy, Part II: A stress rate and temperature dependent anisotropic yield criterion. International Journal of Plasticity, 38, 14–26.

    CrossRef  Google Scholar 

  • Korkolis, Y. P., Kyriakides, S. (2008). An advanced yield function including deformation-induced anisotropy. Inflation and burst of aluminum tubes Part II. International Journal of Plastics, 24, 1625–1637.

    Google Scholar 

  • Kowalewski, Z. L., & Śliwowski, M. (1997). Effect of cyclic loading on the yield surface evolution of 18G2A low-alloy steel. International Journal of Mechanical Sciences, 39(1), 51–68.

    CrossRef  Google Scholar 

  • Kowalsky, U. K., Ahrens, H., & Dinkler, D. (1999). Distorted yield surfaces—Modeling by higher order anisotropic hardening tensors. Computational Materials Science, 16, 81–88.

    CrossRef  Google Scholar 

  • Lankford, W. T., Low, J.R., & Gensamer, M. (1947). The plastic flow of aluminium alloy sheet under combined loads. Transactions of the AIME, 171, 574; TP 2238, Met. Techn.

    Google Scholar 

  • Love, A. E. H. (1944). A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publication.

    MATH  Google Scholar 

  • Luo, M., Dunand, M., & Moth, D. (2012). Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading—Part II: Ductile fracture. International Journal of Plasticity, 32–33, 36–58.

    CrossRef  Google Scholar 

  • Luo, X. Y., Li, M., Boger, R. K., Agnew, S. R., & Wagoner, R. H. (2007). Hardening evolution of AZ31B Mg sheet. International Journal of Plasticity, 23, 44–86.

    CrossRef  MATH  Google Scholar 

  • Malinin, N. N., & Rżysko, J. (1981). Mechanika materiałów. Warszawa: PWN.

    Google Scholar 

  • Nixon, M. E., Cazacu, O., & Lebensohn, R. A. (2010). Anisotropic response of high-purity \(\alpha \)-titanium: Experimental characterization and constitutive modeling. International Journal of Plasticity, 26, 516–532.

    CrossRef  MATH  Google Scholar 

  • Nye, J. F. (1957). Physical Properties of Crystals their Representations by Tensor and Matrices. Oxford: Clarendon Press.

    CrossRef  MATH  Google Scholar 

  • Ottosen, N. S., & Ristinmaa, M. (2005). The Mechanics of Constitutive Modeling. Amsterdam: Elsevier.

    Google Scholar 

  • Plunkett, B., Cazacu, O., & Barlat, F. (2008). Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metal. International Journal of Plasticity, 24, 847–866.

    CrossRef  MATH  Google Scholar 

  • Ralston, T. D. (1977). Yield and Plastic Deformation in ICE Crushing Failure. Seatle, Washington: ICSI. AIDJEX Symposium on Sea Ice-Processes and Models.

    Google Scholar 

  • Rogers, T. G. (1990). Yield criteria, flow rules, and hardening in anisotropic plasticity. In Yielding, Damage and Failure of Anisotropic Solids (pp. 53–79). London: Mechanical Engineering Publication.

    Google Scholar 

  • Rymarz, C. Z. (1993). Continuum Mechanics. Warszawa: PWN.

    Google Scholar 

  • Sayir, M. (1970). Zur Fließbedingung der Plastiztätstheorie. Ingenierarchiv, 39, 414–432.

    CrossRef  MATH  Google Scholar 

  • Skrzypek, J., & Ganczarski, A. (2013). Anisotropic initial yield and failure criteria including temperature effect. In Encyclopedia of Thermal Stresses. Springer Science+Business Media Dordrecht.

    Google Scholar 

  • Sobotka, Z. (1969). Theorie des plastischen Fliessens von anisotropen Körpern. Z. Angew. Math. Mechanik, 49, 25–32.

    CrossRef  MATH  Google Scholar 

  • Spencer, A. J. M. (1971). Theory of invariants. In Continuum Physics (pp. 239–353). Academic Press.

    Google Scholar 

  • Sun, C. T., & Vaidya, R. S. (1996). Prediction of composite properties from a representative volume element. Composites Science Technology, 56, 171–179.

    CrossRef  Google Scholar 

  • Szczepiński, W. (1993). On deformation-induced plastic anisotropy of sheet metals. Archives of Mechanics, 45(1), 3–38.

    MATH  Google Scholar 

  • Tsai, S. T., & Wu, E. M. (1971). A general theory of strength for anisotropic materials. International Journal for Numerical Methods in Engineering, 38, 2083–2088.

    Google Scholar 

  • von Mises, R. (1913). Mechanik der festen Körper im plastisch deformablen Zustand, Götingen Nachrichten. Mathematical Plasticity, 4(1), 582–592.

    MATH  Google Scholar 

  • von Mises, R. (1928). Mechanik der plastischen Formänderung von Kristallen. ZAMM, 8(13), 161–185.

    CrossRef  MATH  Google Scholar 

  • Voyiadjis, G. Z., & Thiagarajan, G. (1995). An anisotropic yield surface model for directionally reinforced metal-matrix composites. International Journal of Plasticity, 11, 867–894.

    CrossRef  MATH  Google Scholar 

  • Westergaard, H. M. (1920). On the resistance of ductile materials to combined stresses in two and three directions perpendicular to one another. Journal of the Franklin Institute, 189, 627–640.

    Google Scholar 

  • Yoon, J. W., Lou, Y., Yoon, J., & Glazoff, M. V. (2014) Asymmetric yield function based on stress invariants for pressure sensitive metals. International Journal of Plasticity.

    Google Scholar 

  • Yoshida, F., Hamasaki, H. M., & Uemori, T. (2013). A user-friendly 3D yield function to describe anisotropy of steel sheets. International Journal of Plasticity, 45, 119–139.

    CrossRef  Google Scholar 

  • Życzkowski, M. (2001). Anisotropic yield conditions. In Handbook of Materials Behavior Models (pp. 155–165). San Diego: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Artur Ganczarski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2023 CISM International Centre for Mechanical Sciences

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Ganczarski, A. (2023). Anisotropy of Yield/Failure Criteria—Comparison of Explicit and Implicit Formulations. In: Altenbach, H., Ganczarski, A. (eds) Advanced Theories for Deformation, Damage and Failure in Materials. CISM International Centre for Mechanical Sciences, vol 605. Springer, Cham. https://doi.org/10.1007/978-3-031-04354-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-04354-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-04352-9

  • Online ISBN: 978-3-031-04354-3

  • eBook Packages: EngineeringEngineering (R0)