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Constitutive Modeling for Metals

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Advanced Methods in Material Forming

Summary

This paper reviews aspects of the plastic behavior common in metals and alloys. Macroscopic and microscopic phenomena occurring during plastic deformation are described succinctly. Constitutive models of plasticity at the micro- and macro-scales, suitable for applications to forming, are discussed in a very broad fashion. Approaches to plastic anisotropy are reviewed in a more detailed manner.

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References

  • Altenpohl D.G., Aluminum: Technology, Applications and Environment, Warrendale, PA, TMS, 1998.

    Google Scholar 

  • Barlat F., Aretz H., Yoon J.W., Karabin M.E., Brem J.C., Dick R.E., “Linear transformation-based anisotropic yield functions”, Int. J. Plasticity, vol. 21, 2005, p. 1009–1039.

    Article  MATH  Google Scholar 

  • Barlat F., Cazacu O., Życzowski M., Banabic D., Yoon J.W., “Yield surface plasticity and anisotropy”, Continuum Scale Simulation of Engineering Materials – Fundamentals – Microstructures – Process Applications, Raabe D., Roters F., Barlat F., Chen L.-Q., (eds.), Berlin, Wiley-VCH Verlag GmbH, 2004, p. 145–177.

    Google Scholar 

  • Barlat F., Liu J., “Modeling precipitate-induced anisotropy in binary Al-Cu alloys”, Mat. Sci. Eng., vol. A257, 1998, p. 47–61.

    Google Scholar 

  • Bate P., Roberts W.T., Wilson D.V., “The plastic anisotropy of two-phase aluminum alloys – I. Anisotropy in unidirectional deformation”, Acta Metall., vol. 29, 1981, p. 1797–1814.

    Article  Google Scholar 

  • Bishop J.W.F., Hill R., “A theory of the plastic distortion of a polycrystalline aggregate under combined stresses”, Phil. Mag., vol. 42, 1951, p. 414–427.

    MATH  MathSciNet  Google Scholar 

  • Boehler J.P., ≪ Lois de Comportement anisotropes des milieux continus ≫ , J. Mécanique, vol. 17, 1978, p. 153–190.

    MATH  MathSciNet  Google Scholar 

  • Bulatov V.V., Richmond O., Glazov M.V., “An atomistic dislocation mechanism of pressure-dependent plastic flow in aluminium”, Acta Materialia, vol. 47, 1999, p. 3507–3514.

    Article  Google Scholar 

  • Cazacu O., Barlat F., “A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals”, Int. J. Plasticity, vol. 20, 2004, p. 2027–2045.

    Article  MATH  Google Scholar 

  • Cazacu O., Barlat F., “Application of the theory of representation to describe yielding of anisotropic aluminum alloys”, Int. J. Eng. Sci., vol. 41, 2003, p. 1367–1385.

    Article  Google Scholar 

  • Cazacu O., Plunkett B., Barlat F., “Orthotropic yield criterion for Mg alloy sheets”, Proceedings of the 8th Conference of the European Scientific Association for Material Forming, Cluj-Napoca, Romania, April 27–29, 2005, Banabic, D., (ed.), Bucharest, The Publishing House of the Romanian Academy, p. 3–10.

    Google Scholar 

  • Chien W.Y, Pan J., Tang S.C., “A combined necking and shear localization analysis for aluminum alloys sheets under biaxial stretching conditions”, Int. J. Plasticity, vol. 20, 2004, p. 1953–1981.

    Article  MATH  Google Scholar 

  • Dafalias Y.F., Popov E.P., “A model of nonlinearly hardening materials for complex loading”, Acta Mechanica, vol. 21, 1975, p. 173–192.

    Article  Google Scholar 

  • Drucker D.C., Prager W., “Soil mechanics and plastic analysis or limit design”, Quart. Appl. Math., vol. 10, 1952, p. 157–165.

    MATH  MathSciNet  Google Scholar 

  • Eshelby J.D., “The determination of the elastic field of an ellipsoidal inclusion and related problems”, Proc. Roy. Soc. London, vol. A241, 1957, p. 376–396.

    MathSciNet  Google Scholar 

  • Estrin Y, “Dislocation density-related constitutive modeling”, Unified Constitutive Law of Plastic Deformation, Krausz A.S., Krausz K. (eds.), Academic Press, San Diego, CA, 1996, p. 69–106.

    Google Scholar 

  • Gambin W., Plasticity and Texture, Amsterdam, Kluwer Academic Publishers, 2001.

    Google Scholar 

  • aGurson A.L., “Continuum theory of ductile fracture by void nucleation and growth – Part I: Yield criteria and flow rules for porous ductile media”, ASME J. Eng. Materials and Technology, vol. 99, 1977, p. 2–15.

    Google Scholar 

  • Hashiguchi K., “Generalized Plastic Flow Rule”, Int. J. Plasticity, vol. 21, 2005, p. 321–351.

    Article  MATH  Google Scholar 

  • Hecker S.S., “Experimental studies of yield phenomena in biaxially loaded metals”, Constitutive Modelling in Viscoplasticity, Stricklin A., Saczalski K.C. (eds.), ASME, New-York, ASME, 1976, p. 1–33.

    Google Scholar 

  • Hershey A.V., “The plasticity of an isotropic aggregate of anisotropic face centred cubic crystals”, J. Appl. Mech., vol. 21, 1954, p. 241–249.

    MATH  Google Scholar 

  • Hoh K.C., Lin J., Dean T.A., “Modeling of springback in creep forming thick aluminum sheets”, Int. J. Plasticity, vol. 20, 2004, p. 733–751.

    Article  Google Scholar 

  • Hosford W.F., Caddell R.M., Metal Forming-Mechanics and Metallurgy, Englewood Cliffs, NJ, Prentice-Hall, Inc., 1983.

    Google Scholar 

  • Hosford W.F., The Mechanics of Crystals and Polycrystals, Oxford, Science Publications, 1993.

    Google Scholar 

  • Jung J., “A note on the influence of hydrostatic pressure on dislocations”, Philos. Mag. A, vol. 43, 1981, p. 1057–1061.

    Google Scholar 

  • Kalidindi S.R., “Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals”, Int. J. Plasticity, vol. 17, 2001, p. 837–860.

    Article  MATH  Google Scholar 

  • Kassner M.E., Hayes T.A., “Creep cavitation in metal”, Int. J. Plasticity, vol. 19, 2003, p. 1715–1864.

    Article  MATH  Google Scholar 

  • Kelley E.W., Hosford W.F., “Deformation characteristics of textured magnesium”, Trans. TMS-AIME, vol. 242, 1968, p. 654–661.

    Google Scholar 

  • Khaleel M.A., Zbib H.M., Nyberg E.A., “Constitutive modeling of deformation and damage in superplastic materials”, Int. J. Plasticity, vol. 17, 2001, p. 277–296.

    Article  MATH  Google Scholar 

  • Kocks U.F., Tomé C.N., Wenk H.-R., Texture and Anisotropy, Cambridge, University Press, 1998.

    Google Scholar 

  • Korbel A., “Structural and mechanical aspects of homogeneous and non-homogeneous deformation in solids”, Localization and Fracture Phenomena in Inelastic Solids, P. Perzyna P. (ed.), Wien, Springer-Verlag, 1998, p. 21–98.

    Google Scholar 

  • Krausz A.S., Krausz K., “The constitutive law of deformation kinetics”, Unified Constitutive Laws of Plastic Deformation, San Diego, CA, Academic Press, (1996), p. 229–279.

    Google Scholar 

  • Krempl E., “A small-strain viscoplasticity theory based on overstress“, Unified Constitutive Laws of Plastic Deformation, Krausz A.S., Krausz K. (eds.), San Diego, CA, Academic Press, (1996), p. 281–318.

    Google Scholar 

  • Kubin L.P., Estrin Y., “Evolution for dislocation densities and the critical conditions for the Portevin-Le Chatelier effect”, Acta Metall. Mater., vol. 38, 1990, p. 697–708.

    Article  Google Scholar 

  • Leblond J.-B., Mécanique de la rupture fragile et ductile, Paris, Lavoisier, 2003.

    MATH  Google Scholar 

  • Lemaitre J. (ed.), Handbook of Materials Behaviour Models, San Diego, Academic Press, San Diego, 2001.

    Google Scholar 

  • Lemaitre J., Chaboche J.-L., Mechanics of Solid Materials, Cambridge, University Press, 1990.

    MATH  Google Scholar 

  • Perocheau F., Driver J., “Slip systems rheology of Al-1 % Mn crystals deformed by hot plane strain compression”, Int. J. Plasticity, vol. 18, 2002, p. 185–203.

    Article  Google Scholar 

  • Raabe D., Roters F., Barlat F., Chen L.Q. (eds.), Continuum Scale Simulations of Engineering Materials – Fundamentals – Microstructures – Process Applications, Berlin, Wiley-VCH Verlag GmbH, 2004.

    Google Scholar 

  • Richmond O. and Spitzig W.A., “Pressure dependence and dilatancy of plastic flow”, IUTAM Conference, Theoretical and Applied Mechanics, Proc. 15mathrm th International Congress of Theoretical and Applied Mechanics, Amsterdam, North-Holland Publishers, 1980, p. 377–386.

    Google Scholar 

  • Rizzi E., Hähner P., “On the Portevin-Le Chatelier effect: Theoretical modeling and numerical results”, Int. J. Plasticity, vol. 20, 2004, p. 121–165.

    Article  MATH  Google Scholar 

  • Siruguet K., Leblond J.-B., “Effect of void locking by inclusions upon the plastic behavior of porous ductile solids – I: Theoretical modeling and numerical study of void growth”, Int. J. Plasticity, vol. 20, 2004a, p. 225–254.

    Article  MATH  Google Scholar 

  • Siruguet K., Leblond J.-B., “Effect of void locking by inclusions upon the plastic behavior of porous ductile solids – part II: Theoretical modeling and numerical study of void coalescence”, Int. J. Plasticity, vol. 20, 2004b, p. 255–268.

    Article  MATH  Google Scholar 

  • Spitzig W.A, “Effect of hydrostatic pressure on plastic flow properties of iron single crystal”, Acta Metall., vol. 27, 1979, p. 523–534.

    Article  Google Scholar 

  • Spitzig W.A, Sober R.J., Richmond O., “The effect of hydrostatic pressure on the deformation behavior of Maraging and HY-80 steels and its implication for plasticity theory”, Metall. Trans., vol. 7A, 1976, p. 1703–1710.

    Google Scholar 

  • Spitzig, W.A., Richmond, O., “The effect of pressure on the flow stress of metals”, Acta Metal., vol. 32, 1984, p. 457–463.

    Article  Google Scholar 

  • Staroselski A., Anand L., “A constitutive model for hcp materials deforming by twinning: Application to magnesium alloy AZ31B”, Int. J. Plasticity, vol. 19, 2003, p. 1843–1864.

    Article  Google Scholar 

  • Taleh L., Sidoroff F., “A micromechanical model of the Greenwood-Johnson mechanism in transformation induced plasticity”, Int. J. Plasticity, vol. 19, 2003, p. 1821–1842.

    Article  Google Scholar 

  • Wilson D.V., “Reversible work-hardening in alloys of cubic metals”, Acta Metall. vol. 13, 1965, 807–814.

    Article  Google Scholar 

  • Zhou Z.-D., Zhao S.-X., Kuang Z.-B., “An integral elasto-plastic constitutive theory”, Int. J. Plasticity, vol. 19, 2003, p. 1377–1400. t

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Alloy Technology and Materials Research Division, Alcoa Inc., Alcoa Technical Center, 100 Technical Drive, Alcoa Center, PA 15069-0001, USA

    F. Barlat

  2. Center for Mechanical Engineering and Automation, University of Aveiro, Campus Universitario de Santiago, P-3810 Aveiro, Portugal

    F. Barlat

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  1. F. Barlat
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© 2007 Springer-Verlag Berlin Heidelberg

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Barlat, F. (2007). Constitutive Modeling for Metals. In: Advanced Methods in Material Forming. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69845-0_1

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  • DOI: https://doi.org/10.1007/3-540-69845-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69844-9

  • Online ISBN: 978-3-540-69845-6

  • eBook Packages: EngineeringEngineering (R0)

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