Skip to main content
Log in

Elastic-plastic-creep response of multilayered systems under cyclic thermo-mechanical loadings

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The modified Ohno and Abdel-Karim nonlinear kinematic hardening model considering cyclic hardening and creep effect are developed to investigate the deformation and residual stress of multilayered systems subjected to cyclic thermal and mechanical loads. Results reveal that, if the creep behavior is considered, significant stress relaxation takes place during about the first several cycles, and the accumulated strain of multilayered systems under deformation-controlled loads finally remains constant, which leads to shakedown. Remarkable changes of the residual stress, location of neutral axis and curvature of Si-Cu beams are observed during about the first 100 cycles. Therefore, the proposed model can be used for the engineering design of multilayered systems under complex loads.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Q. Guo, W. Z. Meng, X. T. Zheng, L. Tian and H. C. Shi, Prediction of stress relaxation from creep data in terms of average creep rate, J. Strain. Anal. Eng., 50 (1) (2015) 15–24.

    Article  Google Scholar 

  2. J. Q. Guo, X. T. Zheng, Y. Zhang, W. H. C. Shi and Z. Meng, A unified continuum damage mechanics model for predicting the stress relaxation behavior of high-temperature bolting, J. Pressure Vessel Technol., 136 (1) (2013) 011203.

    Article  Google Scholar 

  3. J. Q. Guo, F. Li, X. T. Zheng, H. C. Shi and W. Z. Meng, An accelerated method for creep prediction from short term stress relaxation tests, J. Pressure Vessel Technol., 138 (3) (2016) 031401.

    Article  Google Scholar 

  4. X. T. Zheng, C. F. Peng, J. Y. Yu, C. G. Wang and W. Lin, A unified shakedown sssessment method for butt welded joints with various weld groove shapes, J. Pressure Vessel Technol., 137 (2) (2015) 021404.

    Article  Google Scholar 

  5. X. T. Zheng, H. Y. Peng, J. Y. Yu, W. Wang, W. Lin and J. M. Xu, Analytical ratchet limit for pressurized pipeline under cyclic nonproportional loadings, J. Pipeline Syst. Eng. Pract., 8 (3) (2017) 04017002.

    Article  Google Scholar 

  6. X. T. Zheng, K. W. Wu, W. Wang, J. Y. Yu, J. M. Xu and L.W. Ma, Low cycle fatigue and ratcheting behavior of 35CrMo structural steel at elevated temperature, Nucl. Eng. Des., 314 (2017) 285–292.

    Article  Google Scholar 

  7. C. H. Hsueh, Modeling of elastic deformation of multilayers due to residual stresses and external bending, J. Appl. Phys., 91 (12) (2002) 9652–9656.

    Article  Google Scholar 

  8. N. H. Zhang, Thermoelastic stresses in multilayered beams, Thin Solid Films, 515 (23) (2007) 8402–8406.

    Article  Google Scholar 

  9. X. C. Zhang, B. S. Xu and F. Z. Xuan, Residual stresses in the elastoplastic multilayer thin film structures: The cases of Si/Al bilayer and Si/Al/SiO2 trilayer structures, J. Appl. Phys., 103 (2008) 073505.

    Article  Google Scholar 

  10. J. M. Klebanov, Shakedown of creeping structures, Int. J. Solids Struct., 35 (23) (1998) 3121–3133.

    Article  MATH  Google Scholar 

  11. M. A. S. Sadigh, Creep simulation of adhesively bonded joints using modified generalized time hardening model, J. Mech. Sci. Technol., 30 (4) (2016) 1555–1561.

    Article  Google Scholar 

  12. Q. Q. Chen, F. Z. Xuan and S. T. Tu, Residual stress analysis in the film/substrate system with the effect of creep deformation, J. Appl. Phys., 106 (3) (2009) 033512.

    Article  Google Scholar 

  13. Q. Q. Chen, F. Z. Xuan and S. T. Tu, Modeling of creep deformation and its effect on stress distribution in multilayer systems under residual stress and external bending, Thin Solid Films, 517 (9) (2009) 2924–2929.

    Article  Google Scholar 

  14. X. T. Zheng and F. Z. Xuan, Shakedown analysis of multilayered beams coupled with ductile damage, Nucl. Eng. Des., 250 (2012) 14–22.

    Article  Google Scholar 

  15. W. G. Mao, Y. C. Zhou, L. Yang and X. H. Yu, Modeling of residual stresses variation with thermal cycling in thermal barrier coatings, Mech. Mater., 38 (12) (2006) 1118–1127.

    Article  Google Scholar 

  16. M. R. Eslami and M. Shariyat, A technique to distinguish the primary and secondary stresses, J. Pressure Vessel Technol., 117 (3) (1995) 197–203.

    Article  Google Scholar 

  17. H. Mahbadi, A. R. Gowhari and M. R. Eslami, Elasticplastic-creep cyclic loading of beams using the Prager kinematic hardening model, J. Strain. Anal. Eng., 39 (2) (2004) 127–136.

    Article  Google Scholar 

  18. K. Nakane, N. Ohno, M. Tsuda, Y. J. Yagi, I. Nakagawa and T. Atsumi, Thermal ratcheting of solder-bonded elastic and elastoplastic layers, Int. J. Plasticity, 24 (10) (2008) 1819–1836.

    Article  MATH  Google Scholar 

  19. K. Nakane, N. Ohno and H. Tanie, Thermal ratcheting of solder-bonded layered plates: Cyclic recovery and growth of deflection, Comput. Mech., 46 (2) (2009) 259–268.

    Article  MATH  Google Scholar 

  20. D. Y. Kim and S. Y. Han, Effect of interlayer forces for multilayered graphene sheets with different gap thicknesses in using nanoscale molecular mechanics approach, J. Mech. Sci. Technol., 29 (5) (2015) 2111–2120.

    Article  Google Scholar 

  21. A. Maghsoodi, A. Ohadi, M. Sadighi and H. Amindavar, Damage detection in multilayered fiber-metal laminates using guided-wave phased array, J. Mech. Sci. Technol., 30 (5) (2016) 2113–2120.

    Article  Google Scholar 

  22. Muralidhara and R. Rao, Displacement characteristics of a piezoactuator-based prototype microactuator with a hydraulic displacement amplification system, J. Mech. Sci. Technol., 29 (11) (2015) 4817–4822.

    Article  Google Scholar 

  23. J. S. Lee, A new unified modeling of acoustically-coupled multilayers by (u, s, u, W) displacement formulation based poroelastic transfer matrix, J. Mech. Sci. Technol., 29 (2) (2015) 663–676.

    Article  Google Scholar 

  24. N. Ohno and M. Abdel-Karim, Uniaxial ratchetting of 316FR steel at room temperature. Part II. Constitutive modeling and simulation, J. Eng. Mater. Technol., 122 (1) (2000) 35–41.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  26. N. Ohno and N. Wang, Kinematic hardening rules with critical state of dynamic recovery, Part I: Formulation and basic features for ratchetting behavior, Int. J. Plasticity, 9 (3) (1993) 375–390.

    MATH  Google Scholar 

  27. X. Chen and R. Jiao, Modified kinematic hardening rule for multiaxial ratcheting prediction, Int. J. Plasticity, 20 (4) (2004) 871–898.

    Article  Google Scholar 

  28. D. L. Wu, F. Z. Xuan, S. J. Guo and P. Zhao, Uniaxial mean stress relaxation of 9–12% Cr steel at high temperature: Experiments and viscoplastic constitutive modeling, Int. J. Plasticity, 77 (2016) 156–173.

    Article  Google Scholar 

  29. S. L. Zhang and F. Z. Xuan, Interaction of cyclic softening and stress relaxation of 9-12% Cr steel under straincontrolled fatigue-creep condition: Experimental and modeling, Int. J. Plasticity, 98 (2017) 45–64.

    Article  Google Scholar 

  30. F. H. Vitovec, Cavity growth and creep rate taking into account the change of net stress, J. Mater. Sci., 7 (6) (1972) 615–620.

    Article  Google Scholar 

  31. P. J. Henderson and R. Sandström, Low temperature creep ductility of OFHC copper, Mater. Sci. Eng. A, 246 (1–2) (1998) 143–150.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaotao Zheng.

Additional information

Recommended by Associate Editor Heung Soo Kim

Xiao-tao Zheng received his B.S. and M.S. degrees in mechanical engineering from Wuhan Institute of Technology, and Ph.D. degrees in mechanical engineering from East China University of Science and Technology, P.R. China. His research interests include ratcheting effect, creep-fatigue life of high temperature structures and computational mechanics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, X., Wang, J., Wang, W. et al. Elastic-plastic-creep response of multilayered systems under cyclic thermo-mechanical loadings. J Mech Sci Technol 32, 1227–1234 (2018). https://doi.org/10.1007/s12206-018-0226-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-018-0226-5

Keywords

Navigation