Skip to main content
SpringerLink
Log in

Multi-mechanism modeling of proportional and non-proportional ratchetting of stainless steel 304

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This work is devoted to a survey of the multi-mechanism (MM) models proposed in literature during the last two decades. This MM approach is a possible alternative to the wide-spread Chaboche’s model when modeling complex material behavior. Here, the description of the cyclic behavior under complex loading histories is in the focus. The capabilities of two recent versions of the MM models are demonstrated through the simulation of cyclic proportional and non-proportional loading paths under stress or the combination of stress–strain control. The reliability of the two MM models is investigated through the study of the mechanical behavior of a 304 stainless steel (304 SS) at room temperature. Beside the assessment of the stress–strain overall behavior, the local contribution of stress and strains at each mechanism level is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dafalias Y., Popov E.: A model of nonlinearly hardening materials for complex loading. Act. Mech. 21, 173–192 (1975)

    Article  MATH  Google Scholar 

  2. Kujawski D., Mróz Z.: A viscoplastic material model and its application to cyclic loading. Acta Mech. 36, 213–230 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  3. Voyiadjis G., Sivakumar S.: A robust kinematic hardening rule for cyclic plasticity with ratchetting effects part ii. application to nonproportional loading cases. Act. Mech. 107, 117–136 (1994)

    Article  MATH  Google Scholar 

  4. Voyiadjis G., Basuroychowdhury I.: A plasticity model for multiaxial cyclic loading and ratchetting. Acta Mech. 126, 19–35 (1998)

    Article  MATH  Google Scholar 

  5. Chen X., Kim K.S.: Modeling of ratcheting behavior under multiaxial cyclic loading. Acta Mech. 163, 9–23 (2003)

    MATH  Google Scholar 

  6. Colak O.U., Krempl K.: Modeling of uniaxial and biaxial ratcheting behavior of 1026 carbon steel using the simplified viscoplasticity theory based on overstress (VBO). Acta Mech. 160, 27–44 (2003)

    Article  MATH  Google Scholar 

  7. Lissenden C.J., Colaiuta B.A., Lerch J.F.: Hardening behavior of three metallic alloys under combined stresses at elevated temperature. Acta Mech. 169, 53–77 (2004)

    Article  MATH  Google Scholar 

  8. Hashiguchi K., Ueno M., Ozaki T.: Elastoplastic model of metals with smooth elastic–plastic transition. Acta Mech. 223, 985–1013 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hassan T., Kyriakides S.: Ratcheting of cyclically hardening and softening materials: I. Uniaxial behavior. Int. J. Plast. 10, 149–184 (1994)

    Article  MATH  Google Scholar 

  10. Hassan T., Kyriakides S.: Ratcheting of cyclically hardening and softening materials: II. Multiaxial behavior. Int. J. Plast. 10, 185–212 (1994)

    Article  Google Scholar 

  11. Jiang Y., Kurath P.: Nonproportional cyclic deformation: critical experiments and analytical modeling. Int. J. Plast. 13, 743–763 (1997)

    Article  MATH  Google Scholar 

  12. Kang G., Ohno N., Nebu A.: Constitutive modeling of strain range dependent cyclic hardening. Int. J. Plast. 19, 1801–1819 (2003)

    Article  MATH  Google Scholar 

  13. Taheri S., Hauet A., Taleb L., Kpodekon C.: Micro-macro investigations about the fatigue behavior of pre-hardened 304L steel. Int. J. Plast. 27, 1981–2004 (2011)

    Article  MATH  Google Scholar 

  14. Kang G., Kan Q., Zhang J., Sun Y.: Time-dependent ratchetting experiments of SS304 stainless steel. Int. J. Plast. 22, 858–894 (2006)

    Article  Google Scholar 

  15. Kang G.: Ratchetting: recent progresses in phenomenon observation, constitutive modeling and application. Int. J. Fatigue 30, 1448–1472 (2008)

    Article  Google Scholar 

  16. Hassan T., Taleb L., Krishna S.: Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889 (2008)

    Article  MATH  Google Scholar 

  17. Krishna S., Hassan T., Naceur I.B., Saï K., Cailletaud G.: Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304. Int. J. Plast. 25, 1910–1949 (2009)

    Article  Google Scholar 

  18. Taleb L., Hauet A.: Multiscale experimental investigations about the cyclic behavior of the 304L SS. Int. J. Plast. 25, 1359–1385 (2009)

    Article  MATH  Google Scholar 

  19. Abdel-Karim M.: An evaluation for several kinematic hardening rules on prediction of multiaxial stress-controlled ratchetting. Int. J. Plast. 26, 711–730 (2010)

    Article  MATH  Google Scholar 

  20. Abdel-Karim M.: An extension for the Ohno–Wang kinematic hardening rules to incorporate isotropic hardening. Int. J. Pres. Ves. Piping 87, 170–176 (2010)

    Article  Google Scholar 

  21. Taleb L., Cailletaud G.: An updated version of the multimechanism model for cyclic plasticity. Int. J. Plast. 26, 859–874 (2010)

    Article  MATH  Google Scholar 

  22. Noban M., Jahed H., Varvani-Farahani A.: The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach. Int. J. Fatigue 43, 217–225 (2012)

    Article  Google Scholar 

  23. Taleb L.: About the cyclic accumulation of the inelastic strain observed in metals subjected to cyclic stress control. Int. J. Plast. 43, 1–19 (2013)

    Article  Google Scholar 

  24. Zarka, J., Casier, J.: Elastic plastic response of structure to cyclic loading, In: Nemat-Nasser (ed.) Mechanics Today 6. Pergamon Press, New York (1979)

  25. Contesti E., Cailletaud G.: Description of creep plasticity interaction with non unified constitutive equations: application to an austenitic stainless steel. Nucl. Eng. Des. 116, 265–280 (1989)

    Article  Google Scholar 

  26. Cailletaud G., Saï K.: Study of plastic/viscoplastic models with various inelastic mechanisms. Int. J. Plast. 11, 991–1005 (1995)

    Article  MATH  Google Scholar 

  27. Roumagnac P., Guillemer-Néel C., Saanouni K., Clavel M.: Mechanical behaviour and deformation mechanisms of Ni-Ti shape memory alloys in tension. Eur. J. Phys. AP. 10, 109–122 (2000)

    Article  Google Scholar 

  28. Saï K., Aubourg V., Cailletaud G., Strudel J.L.: Physical basis for model with various inelastic mechanisms for nickel base superalloy. Mater. Sci. Technol. 20, 747–755 (2004)

    Article  Google Scholar 

  29. Velay V., Bernhart G., Penazzi L.: Cyclic behavior modeling of a tempered martensitic hot work tool steel. Int. J. Plast. 22, 459–496 (2006)

    Article  MATH  Google Scholar 

  30. Taleb L., Cailletaud G., Blaj L.: Numerical simulation of complex ratcheting tests with a multi-mechanism model type. Int. J. Plast. 22, 724–753 (2006)

    Article  MATH  Google Scholar 

  31. Saï K., Cailletaud G.: Multi-mechanism models for the description of ratchetting: Effect of the scale transition rule and of the coupling between hardening variables. Int. J. Plast. 23, 1589–1617 (2007)

    Article  MATH  Google Scholar 

  32. Kröger N., Böhm M., Wolff M.: Viscoelasticity within the framework of isothermal two-mechanism models. Comput. Math. Sci. 64, 30–33 (2012)

    Article  Google Scholar 

  33. Wolff M., Taleb L.: Consistency for two multi-mechanism models in isothermal plasticity. Int. J. Plast. 24, 2059–2083 (2008)

    Article  MATH  Google Scholar 

  34. Regrain C., Laiarinandrasana L., Toillon S., Saï K.: Multi-mechanism models for semi-crystalline polymer: Constitutive relations and finite element implementation. Int. J. Plast. 25, 1253–1279 (2009)

    Article  MATH  Google Scholar 

  35. Besson J.: Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms. Int. J. Plast. 25, 2204–2221 (2009)

    Article  Google Scholar 

  36. Taleb L., Cailletaud G.: Cyclic accumulation of the inelastic strain in the 304L SS under stress control at room temperature: Ratcheting or creep?. Int. J. Plasticity 27, 1936–1958 (2011)

    Article  MATH  Google Scholar 

  37. Wolff, M., Bökenheide, S., Schlasche, J., Büsing, D., Böhm, M., Zoch, H.: An extended approach to multi-mechanism models in plasticity-theory and parameter identification. Berichte aus der Technomathematik 13-06, Universität Bremen (2013)

  38. Jéridi M., Chouchene H., Keryvin V., Saï K.: Multi-mechanism modeling of amorphous polymers. Mech. Res. Commun. 56, 136–142 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Karlsson B., Sundström B.: Inhomogeneity in plastic deformation of two-phase steels. Mater. Sci. Eng. 16, 161–168 (1974)

    Article  Google Scholar 

  41. Videau J.C., Cailletaud G., Pineau A.: Modélisation des effets mécaniques des transformations de phases. J. de Phys. 4, 227–232 (1994)

    Google Scholar 

  42. Gautier, E., Cailletaud, G.: N-phase modeling applied to phase transformations in steels: a coupled kinetics–mechanics approach, in: ICHMM-2004, Chongqing (China) (2004)

  43. Gallée S., Manach P., Thuillier S.: Mechanical behavior of a metastable austenitic stainless steel under simple and complex loading paths. Mater. Sci. Eng. A 466, 47–55 (2007)

    Article  Google Scholar 

  44. Brusselle-Dupend N., Cangémi L.: A two-phase model for the mechanical behaviour of semicrystalline polymers. Part I: large strains multiaxial validation on HDPE. Mech. Mater. 40, 743–760 (2008)

    Article  Google Scholar 

  45. de Buhan P., Hassen G.: Multiphase approach as a generalized homogenization procedure for modelling the macroscopic behaviour of soils reinforced by linear inclusions. Eur. J. Mech. A/Solids 27, 662–679 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  46. Baudet C., Grandidier J., Cangémi L.: A two-phase model for the diffuso-mechanical behaviour of semicrystalline polymers in gaseous environment. Int. J. Sol. Struct. 46, 1389–1401 (2009)

    Article  MATH  Google Scholar 

  47. Gallée S., Pilvin P.: Deep drawing simulation of a metastable austenitic stainless steel using a two-phase model. J. Math. Proc. Technol. 210, 835–843 (2010)

    Article  Google Scholar 

  48. Hosseininia E.S., Farzaneh O.: A simplified two-phase macroscopic model for reinforced soils. Geot. Geom. 28, 85–92 (2010)

    Article  Google Scholar 

  49. Cleri F.: A two-phase model of large-strain plasticity in covalent nanostructures. Int. J. Plast. 37, 31–52 (2012)

    Article  Google Scholar 

  50. Sayed T.E., Gürses E., Siddiq A.: A phenomenological two-phase constitutive model for porous shape memory alloys. Comput. Math. Sci. 60, 44–52 (2012)

    Article  Google Scholar 

  51. Saï K., Taleb L., Cailletaud G.: Numerical simulation of the anisotropic behavior of 2017 aluminum alloy. Comput. Math. Sci. 65, 48–57 (2012)

    Article  Google Scholar 

  52. Wolff M., Böhm M., Böokenheide S., Kröger N.: Two-mechanism approach in thermo-viscoelasticity with internal variables. Technishe Mechanik 32, 608–621 (2012)

    Google Scholar 

  53. Chaboche, J.L., Dang-Van, K., Cordier, G.: Modelization of strain memory effect on the cyclic hardening of 316 stainless steel, in: SMIRT-5, Division L., Berlin (1979)

  54. Nouailhas D., Chaboche J.L., Savalle S., Cailletaud G.: On the constitutive equations for cyclic plasticity under nonproportional loading. Int. J. Plast. 1, 317–330 (1985)

    Article  Google Scholar 

  55. Ohno N.: A constitutive model of cyclic plasticity with a non-hardening strain region. J. Appl. Mech. 49, 721–727 (1982)

    Article  Google Scholar 

  56. Benallal A., Marquis D.: Constitutive equations for nonproportional cyclic elasto-viscoplasticity. ASME J. Eng. Mater. Technol. 109, 326–336 (1987)

    Article  Google Scholar 

  57. Armstrong, P., Frederick, C.: A mathematical representation of the multiaxial Baushinger effect, in: G.E.C.B., Report RD/B/N 731. (1966)

  58. Burlet, H., Cailletaud, G.: Modelling of cyclic plasticity in finite element codes. In: Proceedings of 2nd International Conference on Constitutive laws for Engineering Materials; Theory and Application, Tucson, AZ (1987)

  59. Besson J., Leriche R., Foerch R., Cailletaud G.: Object-oriented programming applied to the finite element method. Part II. Application to material behaviors. Rev. Eur. EF 7, 567–588 (1998)

    MATH  Google Scholar 

  60. Besson J., Foerch R.: Large scale object-oriented finite element code design. Comp. Methods Appl. Mech. Eng. 142, 165–187 (1997)

    Article  MATH  Google Scholar 

  61. Lamba H., Sidebottom O.: Cyclic plasticity for nonproportional paths, Parts I and II. ASME J. Eng. Mater. Technol. 100, 96–111 (1978)

    Article  Google Scholar 

  62. Cailletaud G., Kaczmarek H., Policella H.: Some elements on multiaxial behavior of 316 stainless steel at room temperature. Mech. Mat. 3, 333–347 (1984)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UGPMM, Ecole Nationale d’Ingénieurs de Sfax, BP 1173, Sfax, Tunisia

    Kacem Saï & Fethi Guesmi

  2. INSA/GPM, CNRS UMR 6634, BP 08 Avenue de l’Université, 76801, Saint Etienne du Rouvray Cedex, France

    Lakhdar Taleb

  3. MINES ParisTech, Centre des Matériaux, CNRS UMR7633, BP 87, 91003, Evry Cedex, France

    Georges Cailletaud

Authors
  1. Kacem Saï
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lakhdar Taleb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fethi Guesmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Georges Cailletaud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kacem Saï.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saï, K., Taleb, L., Guesmi, F. et al. Multi-mechanism modeling of proportional and non-proportional ratchetting of stainless steel 304. Acta Mech 225, 3265–3283 (2014). https://doi.org/10.1007/s00707-014-1108-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1108-2

Keywords

Search

Navigation