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

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Part of the book series: CISM International Centre for Mechanical Sciences ((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.

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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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MATH  Google Scholar 

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

    Book  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  Google Scholar 

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

    Google Scholar 

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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

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

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