Multiaxial ratcheting evaluation of functionally graded cylindrical shell by means of Ohno–Wang’s type models

Abstract

In the present paper, the ratcheting responses of functionally graded (FG) pipe by means of nonlinear kinematic hardening rules of the Ohno–Wang (O–W), McDowell, Jiang–Sehitoglu (J–S) and Chen–Jiao–Kim (C–J–K) models are investigated. The FG pipe is considered to be subjected to a broad class of non-proportional/proportional with different loading types including tension–torsion, tension/thermal–internal pressure with different loading sequences and directions. In the current constitutive models of FG pipe, not only the physical and mechanical properties are variables but also the coefficients of the kinematic hardening rules vary as a power law through thickness. An implicit integration scheme implemented within user subroutine UMAT in ABAQUS/standard is presented for the relatively complicated constitutive models. Comparing with the novel experiments and available results in the literature, the predicted results by the proposed numerical method are demonstrated to be reliable. Results reveal the significant influences of the adopted hardening rules incorporated in the constitutive model and also FG inhomogeneity constant on the multiaxial ratcheting responses of FG pipe.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. 1.

    Abdel-Karim M, Ohno N (2000) Kinematic hardening model suitable for ratchetting with steady-state. Int J Plast 16(3–4):225–240

    MATH  Google Scholar 

  2. 2.

    Armstrong PJ (1966) A mathematical representation of the multiaxial Bauschinger effect. CEBG report RD/B/N, 731

  3. 3.

    Chaboche J-L (1991) On some modifications of kinematic hardening to improve the description of ratchetting effects. Int J Plast 7(7):661–678

    Google Scholar 

  4. 4.

    Chen X, Jiao R, Kim KS (2005) On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel. Int J Plast 21(1):161–184

    MATH  Google Scholar 

  5. 5.

    Jiang Y, Sehitoglu H (1996) Modeling of cyclic ratchetting plasticity, part I: development of constitutive relations. J Appl Mech 63(3):720–725

    MATH  Google Scholar 

  6. 6.

    McDowell D (1995) Stress state dependence of cyclic ratchetting behavior of two rail steels. Int J Plast 11(4):397–421

    Google Scholar 

  7. 7.

    Ohno N, Wang J-D (1993) Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior. Int J Plast 9(3):375–390

    MATH  Google Scholar 

  8. 8.

    Voyiadjis GZ, Al-Rub RKA (2003) Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity. Int J Plast 19(12):2121–2147

    MATH  Google Scholar 

  9. 9.

    Chen X, Shen Y, Fu S, Yu D, Zhang Z, Chen G (2018) Size effects on uniaxial tension and multiaxial ratcheting of oligo-crystalline stainless steel thin wires. Int J Fatigue 116:163–171

    Google Scholar 

  10. 10.

    Hassan T, Taleb L, Krishna S (2008) Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models. Int J Plast 24(10):1863–1889

    MATH  Google Scholar 

  11. 11.

    Kang G, Gao Q, Yang X (2004) Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations. Int J Non-Linear Mech 39(5):843–857

    MATH  Google Scholar 

  12. 12.

    Kim KS, Jiao R, Chen X, Sakane M (2009) Ratcheting of stainless steel 304 under multiaxial nonproportional loading. J Pressure Vessel Technol 131(2):021405

    Google Scholar 

  13. 13.

    Paul SK, Sivaprasad S, Dhar S, Tarafder S (2012) True stress-controlled ratcheting behavior of 304LN stainless steel. J Mater Sci 47(11):4660–4672

    Google Scholar 

  14. 14.

    Taleb L, Keller C (2018) Experimental contribution for better understanding of ratcheting in 304L SS. Int J Mech Sci 146:527–535

    Google Scholar 

  15. 15.

    Singh J, Patel B (2015) Ratcheting analysis of joined conical cylindrical shells. Struct Eng Mech 55(5):913–929

    Google Scholar 

  16. 16.

    Hamidinejad S, Varvani-Farahani A (2015) Ratcheting assessment of steel samples under various non-proportional loading paths by means of kinematic hardening rules. Mater Des 85:367–376

    Google Scholar 

  17. 17.

    Taleb L, Keller C (2017) Experimental contribution for better understanding of ratcheting in 304L SS. Int J Mech Sci 146:527–535

    Google Scholar 

  18. 18.

    Hassan T, Corona E, Kyriakides S (1992) Ratcheting in cyclic plasticity, part II: multiaxial behavior. Int J Plast 8(2):117–146

    Google Scholar 

  19. 19.

    Hassan T, Kyriakides S (1992) Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 8(1):91–116

    Google Scholar 

  20. 20.

    Wang L, Chen G, Zhu J, Sun X, Mei Y, Ling X, Chen X (2014) Bending ratcheting behavior of pressurized straight Z2CND18. 12N stainless steel pipe. Struct Eng Mech 52:1135–1156

    Google Scholar 

  21. 21.

    Houlsby G, Abadie C, Beuckelaers W, Byrne B (2017) A model for nonlinear hysteretic and ratcheting behaviour. Int J Solids Struct 120:67–80

    Google Scholar 

  22. 22.

    Welling CA, Marek R, Feigenbaum HP, Dafalias YF, Plesek J, Hruby Z, Parma S (2017) Numerical convergence in simulations of multiaxial ratcheting with directional distortional hardening. Int J Solids Struct 126:105–121

    Google Scholar 

  23. 23.

    Bouhamed A, Jrad H, Said LB, Wali M, Dammak F (2019) A non-associated anisotropic plasticity model with mixed isotropic–kinematic hardening for finite element simulation of incremental sheet metal forming process. Int J Adv Manuf Technol 100(1–4):929–940

    Google Scholar 

  24. 24.

    Akis T (2009) Elastoplastic analysis of functionally graded spherical pressure vessels. Comput Mater Sci 46(2):545–554

    Google Scholar 

  25. 25.

    Eraslan AN, Akis T (2006) Plane strain analytical solutions for a functionally graded elastic–plastic pressurized tube. Int J Press Vessels Pip 83(9):635–644

    Google Scholar 

  26. 26.

    Jrad H, Mars J, Wali M, Dammak F (2018) Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells. Eng Comput 35(3):833–847

    Google Scholar 

  27. 27.

    Mallek H, Jrad H, Algahtani A, Wali M, Dammak F (2019) Geometrically non-linear analysis of FG-CNTRC shell structures with surface-bonded piezoelectric layers. Comput Methods Appl Mech Eng 347:679–699

    MathSciNet  MATH  Google Scholar 

  28. 28.

    Liu T-J, Zhang C, Wang Y-S, Xing Y-M (2016) The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties. Int J Solids Struct 96:229–239

    Google Scholar 

  29. 29.

    Kar VR, Panda SK (2016) Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel. Chin J Aeronaut 29(1):173–183

    Google Scholar 

  30. 30.

    Mehditabar A, Alashti RA, Pashaei M (2014) Magneto-thermo-elastic analysis of a functionally graded conical shell. Steel Compos Struct 16(1):77–96

    Google Scholar 

  31. 31.

    Mehditabar A, Rahimi G, Sadrabadi SA (2017) Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell. Appl Math Mech 38(4):479–494

    MathSciNet  MATH  Google Scholar 

  32. 32.

    Sahmani S, Fattahi A, Ahmed N (2019) Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL. Eng Comput. https://doi.org/10.1007/s00366-019-00782-5

    Article  Google Scholar 

  33. 33.

    Qin Z, Pang X, Safaei B, Chu F (2019) Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Compos Struct 220:847–860

    Google Scholar 

  34. 34.

    Safaei B, Moradi-Dastjerdi R, Qin Z, Chu F (2019) Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads. Compos B Eng 161:44–54

    Google Scholar 

  35. 35.

    Fattahi A, Safaei B (2017) Buckling analysis of CNT-reinforced beams with arbitrary boundary conditions. Microsyst Technol 23(10):5079–5091

    Google Scholar 

  36. 36.

    Safaei B, Ahmed N, Fattahi A (2019) Free vibration analysis of polyethylene/CNT plates. Eur Phys J Plus 134(6):271

    Google Scholar 

  37. 37.

    Nayebi A (2010) Influence of continuum damage mechanics on the Bree’s diagram of a closed end tube. Mater Des 31(1):296–305

    MathSciNet  Google Scholar 

  38. 38.

    Yu D, Chen G, Yu W, Li D, Chen X (2012) Visco-plastic constitutive modeling on Ohno-Wang kinematic hardening rule for uniaxial ratcheting behavior of Z2CND18 12N steel. Int J Plast 28(1):88–101

    Google Scholar 

  39. 39.

    Ohno N, Wang J-D (1993) Kinematic hardening rules with critical state of dynamic recovery. II: Application to experiments of ratchetting behavior. Int J Plast 9(3):391–403

    MATH  Google Scholar 

  40. 40.

    Jiang Y, Sehitoglu H (1994) Cyclic ratchetting of 1070 steel under multiaxial stress states. Int J Plast 10(5):579–608

    Google Scholar 

  41. 41.

    Jiang Y, Kurath P (1996) Characteristics of the Armstrong–Frederick type plasticity models. Int J Plast 12(3):387–415

    MATH  Google Scholar 

  42. 42.

    Jiang Y, Sehitoglu H (1996) Modeling of cyclic ratchetting plasticity, part II: comparison of model simulations with experiments. J Appl Mech 63(3):726–733

    MATH  Google Scholar 

  43. 43.

    Jiang YSH (1996) Modeling of cyclic ratcheting plasticity, part I: development of constitutive relations. ASME J Appl Mech 63(3):720–725

    MATH  Google Scholar 

  44. 44.

    Bari S, Hassan T (2002) An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation. Int J Plast 18(7):873–894

    MATH  Google Scholar 

  45. 45.

    Bari S, Hassan T (2000) Anatomy of coupled constitutive models for ratcheting simulation. Int J Plast 16(3–4):381–409

    MATH  Google Scholar 

  46. 46.

    Sadrabadi SA, Rahimi G, Citarella R, Karami JS, Sepe R, Esposito R (2017) Analytical solutions for yield onset achievement in FGM thick walled cylindrical tubes undergoing thermomechanical loads. Compos B Eng 116:211–223

    Google Scholar 

  47. 47.

    Zhou D (2015) Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads. Int J Mech Sci 98:70–79

    Google Scholar 

  48. 48.

    Corona E, Hassan T, Kyriakides S (1996) On the performance of kinematic hardening rules in predicting a class of biaxial ratcheting histories. Int J Plast 12(1):117–145

    Google Scholar 

  49. 49.

    Simo JC, Hughes TJ (2006) Computational inelasticity, vol 7. Springer, Berlin

    Google Scholar 

  50. 50.

    Khoei A, Eghbalian M (2012) Numerical simulation of cyclic behavior of ductile metals with a coupled damage–viscoplasticity model. Comput Mater Sci 55:376–389

    Google Scholar 

  51. 51.

    Kobayashi M, Ohno N (1996) Thermal ratchetting of a cylinder subjected to a moving temperature front: effects of kinematic hardening rules on the analysis. Int J Plast 12(2):255–271

    MATH  Google Scholar 

  52. 52.

    Nayebi A, Sadrabadi SA (2013) FGM elastoplastic analysis under thermomechanical loading. Int J Press Vessels Pip 111:12–20

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Aref Mehditabar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mehditabar, A., Rahimi, G.H. Multiaxial ratcheting evaluation of functionally graded cylindrical shell by means of Ohno–Wang’s type models. Engineering with Computers 37, 609–622 (2021). https://doi.org/10.1007/s00366-019-00845-7

Download citation

Keywords

  • Functionally graded materials
  • Ratcheting strain
  • Non-proportional loading
  • Kinematic hardenings