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Scale Transition Rules Applied to Crystal Plasticity

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Materials with Internal Structure

Part of the book series: Springer Tracts in Mechanical Engineering ((STME))

Abstract

Homogenization methods adapted to polycrystalline aggregates are discussed. The description of the transition rule using the self-consistent scheme and based on the assumption of time-independent plasticity are first detailed. A few alternative propositions that simplify the general rate form of the relation given by Hill are also presented, with their limitations. A second part recalls several key ideas used to transfer the problem to time-dependent behavior. A final part is devoted to the comparison of several mean-field models and CPFEM simulations in the case of an equiaxed polycrystalline aggregate with an uniform or heterogeneous local elastic behavior. A significant effect of non-uniform elastic properties is exhibited on the macroscopic behavior, specifically on the apparent yield stress, and also on stress and strain fields.

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References

  1. Abdul-Latif A, Dingli JP, Saanouni K (1998) Modeling of complex cyclic inelasticity in heterogeneous polycrystalline microstructure. Mech Mater 30:287–305

    Article  Google Scholar 

  2. Ausias G, Thuillier S, Omnès B, Wiessner S, Pilvin P (2007) Micro-mechanical model of TPE made of Polypropylene and rubber waste. Polymer 48:3367–3376. doi:http://dx.doi.org/10.1016/j.polymer.2007.03.049

    Google Scholar 

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

    Article  Google Scholar 

  4. Bishop J, Hill R (1951) A theoretical derivation of the plastic properties of a polycrystalline face-centered metal. Philos Mag 42:414–427

    Article  MATH  MathSciNet  Google Scholar 

  5. Budianski B, Wu T (1962) Theoretical prediction of plastic strains of polycrystals. In: Proceedings 4th U.S. national congress of applied mechanics, pp 1175–1185

    Google Scholar 

  6. Busso E, Cailletaud G (2005) On the selection of active slip systems in crystal plasticity. Int J Plast 21:2212–2231

    Article  MATH  Google Scholar 

  7. Cailletaud G (1987) Une approche micromécanique phénoménologique du comportement inélastique des métaux. Ph.D. thesis, Université Pierre et Marie Curie

    Google Scholar 

  8. Cailletaud G, Pilvin P (1994) Utilisation de modèles polycristallins pour le calcul par éléments finis. Revue Européenne des Éléments Finis 3(4):515–541

    MATH  Google Scholar 

  9. Cailletaud G, Saï K (2008) A polycrystalline model for the description of ratchetting: effect of intergranular and intragranular hardening. Mater Sci Eng A 480:24–39

    Article  Google Scholar 

  10. Dingli JP, Abdul-Latif A, Saanouni K (2000) Predictions of the complex cyclic behavior of polycrystals using a self-consistent modeling. Int J Plast 16:411–437

    Article  MATH  Google Scholar 

  11. Doghri I, Adam L, Bilger N (2010) Mean-field homogenization of elasto-viscoplastic composites based on a general incrementally affine linearization method. Int J Plast 26:219–238

    Article  MATH  Google Scholar 

  12. Doghri I, Brassart L, Adam L, Gérard JS (2011) A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites. Int J Plast 27:352–371

    Article  MATH  Google Scholar 

  13. Eshelby J (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond 241:376–396

    Article  MATH  MathSciNet  Google Scholar 

  14. Hashin Z, Shtrikman S (1962) On some variational principles in anisotropic and nonhomogeneous elasticity. J Mech Phys Solids 10:335–342

    Article  MathSciNet  Google Scholar 

  15. Hill R (1965) Continuum micro-mechanisms of elastoplastic polycrystals. J Mech Phys Solids 13:89–101

    Article  MATH  Google Scholar 

  16. Hutchinson J (1966) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc R Soc Lond A348:101–127

    Google Scholar 

  17. Kouddane R, Zouhal N, Molinari A (1994) Complex loading of viscoplastic materials: micro-macro modelling. Mater Sci Eng A175:31–36

    Article  Google Scholar 

  18. Kröner E (1961) Zur plastischen Verformung des Vielkristalls. Acta Metall 9:155–161

    Article  Google Scholar 

  19. Lahellec N, Suquet P (2013) Effective response and field statistics in elasto-plastic and elasto-viscoplastic composites under radial and non-radial loadings. Int J Plast 42:1–30

    Article  Google Scholar 

  20. Lebensohn R, Tomé CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall 41:2611–2624

    Article  Google Scholar 

  21. Lebensohn R, Tomé CN (1994) A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals. Mater Sci Eng A 175:71–82

    Article  Google Scholar 

  22. Lebensohn R, Castaneda PP, Brenner R, Castelnau O (2011) Full-field vs. homogenization methods to predict microstructure-property relations for Polycrystalline materials. In: Ghosh S, Dimiduk D (eds) Computational methods for microstructure-property relationships. Springer, Berlin

    Google Scholar 

  23. Liu Y, Ponte-Castaneda P (2004) Homogenization estimates for the average behavior and field fluctuations in cubic and hexagonal viscoplastic polycrystals. J Mech Phys Solids 52:1175–1211

    Article  MATH  MathSciNet  Google Scholar 

  24. Mareau C, Berbenni S (2015) An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method. Int J Plast 64:134–150

    Article  Google Scholar 

  25. Martin G, Ochoa N, Sai K, Hervé-Luanco E, Cailletaud G (2014) A multiscale model for the elastoviscoplastic behavior of directionally solidified alloys: application to fe structural computations. Int J Solids Struct 51:1175–1187

    Article  Google Scholar 

  26. Masson R, Zaoui A (1999) Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials. J Mech Phys Solids 47:1543–1568

    Article  MATH  MathSciNet  Google Scholar 

  27. Masson R, Bornert N, Suquet M, Zaoui A (2000) An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. J Mech Phys Solids 48:1203–1227

    Article  MATH  MathSciNet  Google Scholar 

  28. Méric L, Cailletaud G (1991) Single crystal modeling for structural calculations. Part 2: finite element implementation. J Eng Mater Technol 113:171–182

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574

    Article  Google Scholar 

  31. Nemat-Nasser S, Obata M (1986) Rate-dependent, finite elasto-plastic deformation of polycrystals. Proc R Soc Lond A 407:343–375

    Article  Google Scholar 

  32. Pan J, Rice JR (1983) Rate sensitivity of plastic flow and implications for yield-surface vertices. Int J Solids Struct 19:973–987

    Article  MATH  Google Scholar 

  33. Paquin A, Sabar H, Berveiller M (1999) Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials. Appl Mech Rev 69:14–35

    MATH  Google Scholar 

  34. Ponte-Castaneda P (1991) The effective mechanical properties of nonlinear isotropic composites. J Mech Phys Solids 39:45–71

    Article  MATH  MathSciNet  Google Scholar 

  35. Ponte-Castaneda P (1996) Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J Mech Phys Solids 44:827–862

    Article  MATH  MathSciNet  Google Scholar 

  36. Rekik A, Allaoui S, Gasser A, Blond E, Adreev K, Sinnema S (2015) Experiments and nonlinear homgenization sustaining mean-field theories for refractory mortarless masonry: the classical secant procedure and its improved variants. Eur J Mech A Solids 49:67–81

    Article  Google Scholar 

  37. Sabar H, Berveiller M, Favier V, Berbenni S (2002) A new class of micro-macro models for elastic-viscoplastic heterogeneous materials. Int J Solids Struct 39:3257–3276

    Article  MATH  MathSciNet  Google Scholar 

  38. Sai K (2011) Multi-mechanism models: present state and future trends. Int J Plast 27:250–281

    Article  Google Scholar 

  39. Sai K, Cailletaud G, Forest S (2006) Micro-mechanical modeling of the inelastic behavior of directionally solidified materials. Mech Mater 38:203–217

    Article  Google Scholar 

  40. Sauzay M (2006) Effet de l’anisotropie élastique cristalline sur la distribution des facteurs de Schmid à la surface des polycristaux. Technical report, Comptes Rendus de Mécanique

    Google Scholar 

  41. Suquet P (1985) Elements of homogeneization for inelastic solid mechanics. In: Sanchez-Palencia E, Zaoui A (eds) Homogeneization techniques for composite media. Springer, New York, pp 193–278

    Google Scholar 

  42. Suquet P (1987) Elements of homogenization for inelastic solid mechanic. In: Homogenization techniques for composite media. Springer, New York, pp 193–278

    Google Scholar 

  43. Suquet P, Lahellec N (2014) Elasto-plasticity of heterogeneous materials at different scales. Procedia IUTAM 10:247–262

    Article  Google Scholar 

  44. Taylor G (1938) Plastic strain in metals. J Inst Met 62:307–324

    Google Scholar 

  45. Weng GJ (1983) Cyclic stress relaxation of polycrystalline metals at elevated temperature. Int J Solids Struct 19(6):541–551

    Article  MATH  Google Scholar 

  46. Yoshida K, Brenner R, Bacroix B, Bouvier S (2009) Effect of regularization of schmid law on self-consistent estimates for rate-independent plasticity of polycrystals. Eur J Mech A Solids 28:905–915

    Article  MATH  Google Scholar 

  47. Zaoui A (1997) Structural morphology and constitutive behaviour of microheterogeneous materials. In: Suquet P (ed) Continuum micromechanic. Springer, New York, pp 291–347

    Chapter  Google Scholar 

  48. Zaoui A, Masson R (2000) Micromechanics-based modeling of plastic polycrystals: an affine formulation. Mater Sci Eng A285:418–424

    Article  Google Scholar 

  49. Zeng T, Shao J, Xu W (2014) Multiscale modeling of cohesive geomaterials with a polycrystalline approach. Mech Mater 69:132–145

    Article  Google Scholar 

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Authors and Affiliations

  1. Centre des Matériaux, Mines ParisTech, 10 rue Henri Desbruères, 91003, Evry, France

    Georges Cailletaud & Florent Coudon

Authors
  1. Georges Cailletaud
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  2. Florent Coudon
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Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Patrizia Trovalusci

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Cailletaud, G., Coudon, F. (2016). Scale Transition Rules Applied to Crystal Plasticity. In: Trovalusci, P. (eds) Materials with Internal Structure. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-21494-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-21494-8_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21493-1

  • Online ISBN: 978-3-319-21494-8

  • eBook Packages: EngineeringEngineering (R0)

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