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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bartlett E (2018) Experimental characterization and modeling of high strength martensitic steels based on a new distortional hardening model. University of Florida
Billington EW (1977) Non-linear mechanical response of various metals. II permanent length changes in twisted tubes. J Phys Appl Phys 10:533–552
Billington EW (1977) Non-linear mechanical response of various metals: I permanent length changes in twisted tubes. J Phys Appl Phys 10:519–531
Billington EW (1977) Non-linear mechanical response of various metals: III permanent length changes in twisted tubes. J Phys Appl Phys 10:553–569
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
Böhlke T, Bertram A, Krempl E (2003) Modeling of deformation induced anisotropy in free-end torsion. Int J Plast 19:1867–1884
Budiansky B, Wu TT (1961) Theoretical prediction of plastic strains of polycrystals. DTIC Document
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
Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal closed packed metals. Int J Plast 22:1171–1194
Cazacu O, Revil-Baudard B, Barlat F (2013) New interpretation of monotonic Swift effects: role of tension–compression asymmetry. Mech Mater 57:42–52
Cazacu O, Revil-Baudard B, Barlat F (2014) New interpretation of cyclic Swift effects. Eur J Mech A/Solids 44:82–90
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
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
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
Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. ASME J Appl Mech 16:349–357
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
Green AE, Naghdi PM (1965) A general theory of an elastic-plastic continuum. Arch Ration Mech Anal 18:251–281
Hassan T, Kyriakides S (1992) Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 8:91–116
Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals. ASME J Appl Mech 21:241–249
Hershey AV (1954) The elasticity of an isotropic aggregate of anisotropic cubic crystals. ASME J Appl Mech 21:236–240
Hill R (1950) The mathematical theory of plasticity. Oxford University Press, Oxford, USA
Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech 39:607–609
Hosford WF (1993) The mechanics of crystals and textured polycrystals. Oxford University Press, Oxford, USA
Hosford WF, Allen T (1973) Twinning and directional slip as a cause for a strength differential effect. Metall Mater Trans B 4:1424–1425
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
Hutchinson J (1964) Plastic stress-strain relations of FCC polycrystalline metals hardening according to Taylor’s rule. J Mech Phys Solids 12:11–24
Hutchinson J (1964) Plastic deformation of bcc polycrystals. J Mech Phys Solids 12:25–33
Kelley E, Hosford WF (1968) The deformation characteristics of textured magnesium. Trans Met Soc AIME 242
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
Kröner E (1961) Zur plastischen verformung des vielkristalls. Acta Metall 9:155–161
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
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
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
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
Nemat-Nasser S (1982) On finite deformation elasto-plasticity. Int J Solids Struct 18:857–872
Nicholas T (1980) Dynamic tensile testing of structural materials using a split Hopkinson bar apparatus. DTIC Document
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
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
Swift H (1947) Length changes in metals under torsional overstrain. Engineering 163:1958
Taylor GI, Quinney H (1932) The plastic distortion of metals. Philos Trans R Soc Lond Ser Contain Pap Math Phys Character 230:323–362
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
Tresca H (1868) Memoire sur l’ecoulement des corps solides, par M. H. Tresca. Imprimerie Imperiale, Paris
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
von Mises R (1913) Mechanik der festen Körper im plastisch deformablen Zustand. Nachrichten Von Ges Wiss Zu Gött Math-Phys Kl 1913:582–592
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-92922-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92921-7
Online ISBN: 978-3-319-92922-4
eBook Packages: EngineeringEngineering (R0)