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Self-Consistent Modelling of Plastic and Viscoplastic Polycrystalline Materials

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Large Plastic Deformation of Crystalline Aggregates

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 376))

Abstract

This lecture describes some self-consistent approaches that are used to model the plastic deformation of strain-rate dependent and of rate-independent polycrystalline materials. A discussion is presented of the grain-matrix interaction law, which in most of the approaches appears to be too stiff. Large strain deformations are considered, and the evolution of the crystallographic texture and of the morphology of grains is accounted for to model the development of the overall anisotropy of the polycrystal.

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References

  • Ahzi, S, A. Molinari and G.R. Canova: Effects of the grain shape on the texture evolution in polycrystalline materials, in: Yielding, Damage and Failure of Anisotropic Solids (Ed. J.P. Boehler), EGF Publication 5 (1990), 425–441.

    Google Scholar 

  • Anand, L. and M. Kothari: A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids, 44 (1996), 525–558.

    Article  Google Scholar 

  • Asaro, R.J. and J.R. Rice: Strain localization in ductile single crystals, J. Mech. Phys. Solids, 25 (1977), 309–338.

    Article  Google Scholar 

  • Asaro, R.J., A. Needleman: Texture development and strain hardening in rate dependent polycrystals, Acta Metall 33 (1985), 923–953.

    Article  Google Scholar 

  • Asaro, R.J.: Micromechanics of crystals and polycrystals, Adv. Applied Mech., 23 (1983), 1–115.

    Google Scholar 

  • Asaro, R.J.: Crystal plasticity, J. Appl. Mech. Trans. ASME, 50 (1983), 921–934.

    Article  Google Scholar 

  • Berveiller M. and A. Zaoui: An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids, 26 (1979), 325–344.

    Article  Google Scholar 

  • Budianski, B. and Wu: Theoretical prediction of plastic strains of polycrystals, in Proc. of the 4th U.S. National Congress of Applied Mechanics, ASME (1962), 1175.

    Google Scholar 

  • Castelnau, O., P. Duval, R.A. Lebensohn and G.R. Canova: Viscoplastic modeling of texture development in polycrystalline ice with a self-consistent approach: comparison with bound estimates, J. Geophys. Res., B6, 101 (1996), 13851–13868.

    Article  Google Scholar 

  • Dahoun, A., G.R. Canova, A. Molinari, M.J. Philippe and C. G’Sell: The modeling of large strain textures and stress-strain relations of polyethylene, Textures and Microstructures, 1418 (1991), 347–354.

    Article  Google Scholar 

  • Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion,and related problems; Proc. Roy. Soc. London, A241 (1957), 376.

    Article  Google Scholar 

  • François, D., A. Pineau and A. Zaoui: Comportement mécanique des matériaux, Vol. 1 (1991), Paris, Hermès.

    Google Scholar 

  • Gilormini, P., and Y. Germain: Int. J. Solids Struct., 23 (1987), 413.

    Article  Google Scholar 

  • Havner, K.S.: Finite deformation of Crystalline Solids. London: Cambridge University Press (1992).

    Book  Google Scholar 

  • Hill, R.: Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13 (1965), 89.

    Article  Google Scholar 

  • Hill, R.: Proc. Roy. Soc. London, A 326 (1972), 131–147.

    Article  Google Scholar 

  • Hill, R. and J. Rice: Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20 (1972), 401–413.

    Article  Google Scholar 

  • Honneff, H. and H; Mecking: Proc. 5th Int. Conf. on Textures of Materials, ICOTOM 5 (Ed. G. Gottstein and K. Lücke), Vol. 1 (1978), 265.

    Google Scholar 

  • Hutchinson, J.W.: Elastic-plastic behavior of polycrystalline metals and composites, Proc. Roy. Soc. London, A319 (1970), 247.

    Article  Google Scholar 

  • Hutchinson, J.W.: Bounds and self-consistent estimate for creep of polycrystalline materials, Proc. Roy. Soc., A348 (1976), 101.

    Article  Google Scholar 

  • Iwakuma, T. and S. Nemat-Nasser: Finite elastic-plastic deformation of polycrystalline metals, Proc. Roy. Soc. London, A394 (1984), 87–119.

    Article  Google Scholar 

  • Kalidindi, S.R., C.A. Bronkhorst and L. Anand: J. Mech. Phys. Solids, 40 (1992), 537.

    Article  Google Scholar 

  • Kouddane, R., A. Molinari and G.R. Canova: Self consistent modelling of heterogeneous viscoelastic and elastoviscoplastic materials, in: Large plastic deformations, Fundamentals and application of metal forming (Ed. C. Teodosiu et al.), Balkema (1993), 129–141.

    Google Scholar 

  • Kröner, E.: Zur plastichen Verformung des Vielkristalls, Acta Metall., 9 (1961), 155.

    Article  Google Scholar 

  • Kröner, E.: Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids, 25 (1977), 137–155.

    Article  Google Scholar 

  • Lebensohn, R.A. and C.N. Tomé: A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys, Acta Metall. et Mater., 41 (1993), 2611–2624.

    Article  Google Scholar 

  • Lee, E.H.: Elastic-plastic deformation at finite strains, J. Appl. Mech. Trans. ASME, 36 (1969), 1–6.

    Article  Google Scholar 

  • Lipinski, P., J. Krier and M. Berveiller: Elastoplasticité des métaux en grandes déformations: comportement global et évolution de la structure interne, Revue Phys. Appl., 25 (1990), 361.

    Google Scholar 

  • Lipinski, P., A. Naddari and M. Berveiller: Recent results concerning the modelling of polycrystalline plasticity at large strains, Int. J. Solids Structure, 29 (1992), 1873–1881.

    Article  Google Scholar 

  • Mandel, J.: Thermodynamics and Plasticity, Proc. of the International Symposium on Foundations of Continuum Thermodynamics (Ed. Delgado Domingos, J.J.; Nina, M.N.R.; Whitelaw, J.H.), pp 283–311. London: Mc Millan Publ.

    Google Scholar 

  • Molinari, A., G.R. Canova and S. Ahzi: A self-consistent approach of the large deformation polycrystal viscoplasticity, Acta Metall., 35 (1987), 2983–2994.

    Article  Google Scholar 

  • Molinari, A., and L. Toth: Tuning a self-consistent viscoplastic model by finite element results I: Modeling, Acta Metall. Mater., 42 (1994), 2453–2458.

    Google Scholar 

  • Molinari, A., S. Ahzi and R. Kouddane: On the self-consistent modeling of elastic-plastic behavior of polycrystals, Mech. of Materials (1997) to appear.

    Google Scholar 

  • Nemat-Nasser, S.: Int. J. Solids Struct., 18 (1982), 857–872.

    Article  Google Scholar 

  • Nemat-Nasser, S. and M. Obata: Rate-dependent, finite elasto-plastic deformation of polycrystals, Proc. Roy. Soc. London, A407 (1986), 343.

    Article  Google Scholar 

  • Rice, J.R.: Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19 (1971), 433–455.

    Article  Google Scholar 

  • Rougier, Y., C. Stolz and A. Zaoui: Self-consistent modelling of elastic-viscoplastic polycrystals, C.R. Acad. Sci. Paris, 318, Série II (1994), 145–151.

    Google Scholar 

  • Takeshita, T., H.R. Wenk, G.R. Canova and A. Molinari: Simulation of dislocation assisted plastic deformation in olivine polycrystals, in: Deformation processes in minerals, ceramics and rocks (Ed. D.J. Barker and P.G. Meredith) Unwin Hyman (1990), 365–374.

    Chapter  Google Scholar 

  • Taylor, G.I. and C.F. Elam: Proc. R. Soc. Lond. A102 (1923), 643. Taylor, G.I. and C.F. Elam: Proc. R. Soc. Lond. A108 (1925), 28. Taylor, G.I.: Plastic strain in metals, J. Inst. Metals, 62 (1938), 307–324.

    Google Scholar 

  • Teodosiu, C.: A dynamical theory of dislocations and its applications to the theory of the elastic-plastic continuum, Proc. Int. Conf. Fundamental Aspects of Dislocation Theory, Washington, 1969 (Eds. J.A. Simmons, R. de Wit, R. Bullough), Nat. Bur. Stand. Spec. Publ. 317 (1970), 837–876.

    Google Scholar 

  • Tomé, C.N., R.A. Lebensohn and U.F. Kocks: A model for texture development dominated by deformation twinning: application to zirconium alloys, Acta metall. mater., 39 (1991), 2667–2680.

    Article  Google Scholar 

  • Toth, L.S., J.J. Jonas, D. Daniel and J.A. Bailey: Text. Microstructures, 19 (1992), 245.

    Article  Google Scholar 

  • Toth, L. and A. Molinari: Tuning a self-consistent viscoplastic model by finite element results I I: Application to torsion textures, Acta metall. mater., 42 (1994), 2459–2466.

    Article  Google Scholar 

  • Van Houtte, P.: Acta metall., 26 (1978), 591.

    Article  Google Scholar 

  • Wagner, F., G.R. Canova, P. Van Houtte and A. Molinari: Comparison of simulated and experimental deformation textures for BCC metals, Textures and Microstructures, 14–18 (1991), 1135–1140.

    Article  Google Scholar 

  • Weng, G.J.: Self-consistent determination of time-dependent behavior of metals, J. of Applied Mech., 48 (1981), 41–46.

    Article  Google Scholar 

  • Wenk, H.R., G.R. Canova, A. Molinari and H. Mecking: Texture development in halite: comparison of Taylor model and self-consistent theory, Acta metall., 37 (1989), 2017–2029.

    Article  Google Scholar 

  • Wenk, H.R., K. Bennett, G.R. Canova and A. Molinari: Modelling plastic deformation of Peridotite with the self-consistent theory, J. Geophys. Res., 96, B5 (1991), 8337–8349.

    Google Scholar 

  • Zaoui, A.: Matériaux hétérogènes et composites (1996), Ecole Polytechnique, Paris.

    Google Scholar 

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Authors and Affiliations

  1. LPMM-CNRS, University of Metz, Metz, France

    A. Molinari

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  1. A. Molinari
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Editors and Affiliations

  1. CNRS, University of Paris-Nord, France

    C. Teodosiu

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© 1997 Springer-Verlag Wien

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Molinari, A. (1997). Self-Consistent Modelling of Plastic and Viscoplastic Polycrystalline Materials. In: Teodosiu, C. (eds) Large Plastic Deformation of Crystalline Aggregates. International Centre for Mechanical Sciences, vol 376. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2672-1_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2672-1_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82909-7

  • Online ISBN: 978-3-7091-2672-1

  • eBook Packages: Springer Book Archive

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