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Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 253))

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Abstract

Chapter 4 is devoted to modeling the plastic behavior of isotropic polycrystalline metallic materials. A review of the classic yield criteria and corresponding stress-based plastic potentials with discussion concerning the predicted mechanical response for various three-dimensional loadings is presented along with the most recent contributions devoted to the description of the behavior of incompressible materials displaying tension–compression asymmetry. On the basis of these new models, a new interpretation and explanation of the Swift phenomenon, occurring in monotonic and cyclic free-end torsion are provided.

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References

  1. Bartlett E (2018) Experimental characterization and modeling of high strength martensitic steels based on a new distortional hardening model. University of Florida

    Google Scholar 

  2. Billington EW (1977) Non-linear mechanical response of various metals. II permanent length changes in twisted tubes. J Phys Appl Phys 10:533–552

    Article  Google Scholar 

  3. Billington EW (1977) Non-linear mechanical response of various metals: I permanent length changes in twisted tubes. J Phys Appl Phys 10:519–531

    Article  Google Scholar 

  4. Billington EW (1977) Non-linear mechanical response of various metals: III permanent length changes in twisted tubes. J Phys Appl Phys 10:553–569

    Article  Google Scholar 

  5. Bishop J, Hill R (1951) XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Lond Edinb Dublin Philos Mag J Sci 42:414–427

    Article  Google Scholar 

  6. Böhlke T, Bertram A, Krempl E (2003) Modeling of deformation induced anisotropy in free-end torsion. Int J Plast 19:1867–1884

    Article  Google Scholar 

  7. Budiansky B, Wu TT (1961) Theoretical prediction of plastic strains of polycrystals. DTIC Document

    Google Scholar 

  8. Cazacu O, Barlat F (2004) A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals. Int J Plast 20:2027–2045

    Article  Google Scholar 

  9. Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal closed packed metals. Int J Plast 22:1171–1194

    Article  Google Scholar 

  10. Cazacu O, Revil-Baudard B, Barlat F (2013) New interpretation of monotonic Swift effects: role of tension–compression asymmetry. Mech Mater 57:42–52

    Article  Google Scholar 

  11. Cazacu O, Revil-Baudard B, Barlat F (2014) New interpretation of cyclic Swift effects. Eur J Mech A/Solids 44:82–90

    Article  MathSciNet  Google Scholar 

  12. Chin GY, Mammel WL, Dolan MT (1969) Taylor analysis for 111 (112) twinning and 111 (110) slip under conditions of axisymmetric flow. Trans Metall Soc AIME 245:383–388

    Google Scholar 

  13. Colak OU (2004) Modeling of the monotonic and cyclic swift effects using anisotropic finite viscoplasticity theory based on overstress (AFVBO): part I—constitutive model. Int J Solids Struct 41:5301–5311

    Article  Google Scholar 

  14. Colak OU (2004) Modeling of monotonic and cyclic Swift effect using anisotropic finite viscoplasticity theory based on overstress (AFVBO): part II—numerical experiments. Int J Solids Struct 41:5313–5325

    Article  Google Scholar 

  15. Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. ASME J Appl Mech 16:349–357

    MathSciNet  MATH  Google Scholar 

  16. Duchêne L, El Houdaigui F, Habraken AM (2007) Length changes and texture prediction during free end torsion test of copper bars with FEM and remeshing techniques. Int J Plast 23:1417–1438

    Article  Google Scholar 

  17. Green AE, Naghdi PM (1965) A general theory of an elastic-plastic continuum. Arch Ration Mech Anal 18:251–281

    Article  MathSciNet  Google Scholar 

  18. Hassan T, Kyriakides S (1992) Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 8:91–116

    Article  Google Scholar 

  19. Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals. ASME J Appl Mech 21:241–249

    MATH  Google Scholar 

  20. Hershey AV (1954) The elasticity of an isotropic aggregate of anisotropic cubic crystals. ASME J Appl Mech 21:236–240

    MATH  Google Scholar 

  21. Hill R (1950) The mathematical theory of plasticity. Oxford University Press, Oxford, USA

    MATH  Google Scholar 

  22. Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech 39:607–609

    Article  Google Scholar 

  23. Hosford WF (1993) The mechanics of crystals and textured polycrystals. Oxford University Press, Oxford, USA

    Google Scholar 

  24. Hosford WF, Allen T (1973) Twinning and directional slip as a cause for a strength differential effect. Metall Mater Trans B 4:1424–1425

    Article  Google Scholar 

  25. Hughes TJ (1984) Numerical implementation of constitutive models: rate-independent deviatoric plasticity. In: Theoretical foundation for large-scale computations for nonlinear material behavior. Springer, Dordrecht, pp 29–63

    Chapter  Google Scholar 

  26. Hutchinson J (1964) Plastic stress-strain relations of FCC polycrystalline metals hardening according to Taylor’s rule. J Mech Phys Solids 12:11–24

    Article  Google Scholar 

  27. Hutchinson J (1964) Plastic deformation of bcc polycrystals. J Mech Phys Solids 12:25–33

    Article  Google Scholar 

  28. Kelley E, Hosford WF (1968) The deformation characteristics of textured magnesium. Trans Met Soc AIME 242

    Google Scholar 

  29. Koiter WT (1953) Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface. Q Appl Math 11:350–354

    Article  MathSciNet  Google Scholar 

  30. Kröner E (1961) Zur plastischen verformung des vielkristalls. Acta Metall 9:155–161

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. Lebensohn R, Turner P, Signorelli J, Canova G, Tomé C (1998) Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model. Model Simul Mater Sci Eng 6:447

    Article  Google Scholar 

  33. Lode W (1926) Versuche über den Einflu\s s der mittleren Hauptspannung auf das Flie\s sen der Metalle Eisen, Kupfer und Nickel. Z Für Phys 36:913–939

    Article  Google Scholar 

  34. Montheillet F, Cohen M, Jonas J (1984) Axial stresses and texture development during the torsion testing of Al, Cu and α-Fe. Acta Metall 32:2077–2089

    Article  Google Scholar 

  35. Nemat-Nasser S (1982) On finite deformation elasto-plasticity. Int J Solids Struct 18:857–872

    Article  Google Scholar 

  36. Nicholas T (1980) Dynamic tensile testing of structural materials using a split Hopkinson bar apparatus. DTIC Document

    Google Scholar 

  37. Revil-Baudard B, Chandola N, Cazacu O, Barlat F (2014) Correlation between Swift effects and tension–compression asymmetry in various polycrystalline materials. J Mech Phys Solids 70:104–115

    Article  Google Scholar 

  38. Spitzig WA, Sober RJ, Richmond O (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall Trans A 7:1703–1710

    Article  Google Scholar 

  39. Swift H (1947) Length changes in metals under torsional overstrain. Engineering 163:1958

    Google Scholar 

  40. Taylor GI, Quinney H (1932) The plastic distortion of metals. Philos Trans R Soc Lond Ser Contain Pap Math Phys Character 230:323–362

    Article  Google Scholar 

  41. Toth L, Jonas J, Gilormini P, Bacroix B (1990) Length changes during free end torsion: a rate sensitive analysis. Int J Plast 6:83–108

    Article  Google Scholar 

  42. Tresca H (1868) Memoire sur l’ecoulement des corps solides, par M. H. Tresca. Imprimerie Imperiale, Paris

    Google Scholar 

  43. Vitek V, Mrovec M, Bassani J (2004) Influence of non-glide stresses on plastic flow: from atomistic to continuum modeling. Mater Sci Eng, A 365:31–37

    Article  Google Scholar 

  44. von Mises R (1913) Mechanik der festen Körper im plastisch deformablen Zustand. Nachrichten Von Ges Wiss Zu Gött Math-Phys Kl 1913:582–592

    MATH  Google Scholar 

  45. Wang C-C (1970) A new representation theorem for isotropic functions: an answer to Professor GF Smith’s criticism of my papers on representations for isotropic functions. Arch Ration Mech Anal 36:166–197

    Article  Google Scholar 

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Cazacu, O., Revil-Baudard, B., Chandola, N. (2019). Yield Criteria for Isotropic Polycrystals. In: Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. Solid Mechanics and Its Applications, vol 253. Springer, Cham. https://doi.org/10.1007/978-3-319-92922-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-92922-4_4

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