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Comparative study of various hardening models for the prediction of plastic responses under strain path change conditions

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Abstract

This work is aimed at investigating the influence of hardening models on the prediction of plastic responses of sheet metals under strain path change conditions. An enhanced back-stress restoration evolution hardening model was proposed, considering that the back stress accumulated in preloading stages was restored gradually in the subsequent loading stage. A comparative study was conducted between the proposed model and other two hardening models, i.e. Chaboche combined hardening model and Yoshida-Uemori hardening model, in terms of their prediction accuracy of work-hardening and r-value evolution behaviors under reverse and orthogonal loading conditions. The parameters in the models were determined by the experimental results of uniaxial tension and uniaxial compression-tension-compression tests using 6061O aluminum sheet. Associated with the Yld2000-2d yield function, these three hardening models were further employed to simulate a two-stage deep drawing process of a cylindrical cup. The predicted punch load-stroke curves, the height distribution of the drawn cup, and the split-ring springback were compared with the experimental ones. Obvious difference between the predictions was observed in the second drawing stage, which indicates the significant influence of hardening model on the prediction of plastic response under strain path change conditions. Among these three hardening models, the proposed hardening model presented a good prediction result which matched well with the experimental outcome.

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References

  1. Peng J, Li K, Dai Q, Peng J (2018) Mechanical properties of pre-strained austenitic stainless steel from the view of energy density. Results Phys 10:187–193. https://doi.org/10.1016/j.rinp.2018.05.034

    Article  Google Scholar 

  2. Lee J, Ha J, Bong HJ et al (2016) Evolutionary anisotropy and flow stress in advanced high strength steels under loading path changes. Mater Sci Eng A 672:65–77. https://doi.org/10.1016/j.msea.2016.06.074

    Article  Google Scholar 

  3. Ha J, Lee J, Kim JH et al (2017) Investigation of plastic strain rate under strain path changes in dual-phase steel using microstructure-based modeling. Int J Plast 93:89–111. https://doi.org/10.1016/j.ijplas.2017.02.005

    Article  Google Scholar 

  4. Hahm JH, Kim KH (2008) Anisotropic work hardening of steel sheets under plane stress. Int J Plast 24:1097–1127. https://doi.org/10.1016/j.ijplas.2007.08.007

    Article  MATH  Google Scholar 

  5. Prager W (1956) A New method of analyzing stresses and strains in work-hardening plastic solids. J Appl Mech 23:493–496

    Article  MathSciNet  Google Scholar 

  6. Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauschinger effect. CEGB Report RD/B/N 731. Central Electricity Generating Board, Berkeley

    Google Scholar 

  7. Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188. https://doi.org/10.1016/0749-6419(86)90010-0

    Article  MATH  Google Scholar 

  8. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int J Plast 18:661–686. https://doi.org/10.1016/S0749-6419(01)00050-X

    Article  MATH  Google Scholar 

  9. Hajbarati H, Zajkani A (2019) A novel analytical model to predict springback of DP780 steel based on modified Yoshida-Uemori two-surface hardening model. Int J Mater Form 12:441–455. https://doi.org/10.1007/s12289-018-1427-2

    Article  Google Scholar 

  10. Lin J, Hou Y, Min J et al (2020) Effect of constitutive model on springback prediction of MP980 and AA6022-T4. Int J Mater Form 13:1–13. https://doi.org/10.1007/s12289-018-01468-x

    Article  Google Scholar 

  11. Zhang W, Zhuang X, Zhang Y, Zhao Z (2020) An enhanced François distortional yield model: Theoretical framework and experimental validation. Int J Plast 127:102643. https://doi.org/10.1016/j.ijplas.2019.102643

    Article  Google Scholar 

  12. Barlat F, Ha J, Grácio JJ et al (2013) Extension of homogeneous anisotropic hardening model to cross-loading with latent effects. Int J Plast 46:130–142. https://doi.org/10.1016/j.ijplas.2012.07.002

    Article  Google Scholar 

  13. He J, Gu B, Li Y, Li S (2018) Forming limits under stretch-bending through distortionless and distortional anisotropic hardening. J Manuf Sci Eng 140:121013. https://doi.org/10.1115/1.4041329

    Article  Google Scholar 

  14. Lee J, Bong HJ, Kim D, Lee M-G (2020) Modeling differential permanent softening under strain-path changes in sheet metals using a modified distortional hardening model. Int J Plast 133:102789. https://doi.org/10.1016/j.ijplas.2020.102789

    Article  Google Scholar 

  15. Qin J, Holmedal B, Zhang K, Hopperstad OS (2017) Modeling strain-path changes in aluminum and steel. Int J Solids Struct 117:123–136. https://doi.org/10.1016/j.ijsolstr.2017.03.032

    Article  Google Scholar 

  16. Zaman SB, Barlat F, Kim JH (2018) Deformation-induced anisotropy of uniaxially prestrained steel sheets. Int J Solids Struct 134:20–29. https://doi.org/10.1016/j.ijsolstr.2017.10.029

    Article  Google Scholar 

  17. Barlat F, Brem JC, Yoon JW et al (2003) Plane stress yield function for aluminum alloy sheets - Part 1: Theory. Int J Plast 19:1297–1319. https://doi.org/10.1016/S0749-6419(02)00019-0

    Article  MATH  Google Scholar 

  18. Yang Y, Vincze G, Baudouin C et al (2021) Strain-path dependent hardening models with rigorously identical predictions under monotonic loading. Mech Res Commun 114:103615. https://doi.org/10.1016/j.mechrescom.2020.103615

    Article  Google Scholar 

  19. Yang H, Zhang W, Zhuang X, Zhao Z (2020) Calibration of Chaboche Combined Hardening Model for Large Strain Range. Procedia Manufacturing. Procedia Manufacturing, Cottbus, pp. 867–872

    Google Scholar 

  20. Nath A, Ray KK, Barai SV (2019) Evaluation of ratcheting behaviour in cyclically stable steels through use of a combined kinematic-isotropic hardening rule and a genetic algorithm optimization technique. Int J Mech Sci 152:138–150. https://doi.org/10.1016/j.ijmecsci.2018.12.047

    Article  Google Scholar 

  21. Schmitt JH, Aernoudt E, Baudelet B (1985) Yield loci for polycrystalline metals without texture. Mater Sci Eng 75:13–20. https://doi.org/10.1016/0025-5416(85)90173-9

    Article  Google Scholar 

  22. Mánik T, Holmedal B, Hopperstad OS (2015) Strain-path change induced transients in flow stress, work hardening and r-values in aluminum. Int J Plast 69:1–20. https://doi.org/10.1016/j.ijplas.2015.01.004

    Article  Google Scholar 

  23. Qin J, Holmedal B, Hopperstad OS (2019) Experimental characterization and modeling of aluminum alloy AA3103 for complex single and double strain-path changes. Int J Plast 112:158–171. https://doi.org/10.1016/j.ijplas.2018.08.011

    Article  Google Scholar 

  24. Bari S, Hassan T (2000) Anatomy of coupled constitutive models for ratcheting simulation. Int J Plast 16:381–409. https://doi.org/10.1016/S0749-6419(99)00059-5

    Article  MATH  Google Scholar 

  25. Rahman SM, Hassan T, Ranjithan SR (2005) Automated parameter determination of advanced constitutive models. In: Proceedings of PVP2005: 2005 ASME Pressure Vessels and Piping Division Conference. pp 1–12

  26. Zhang W, Yang H, Zhuang X et al (2020) Crack initiation prediction eliminating the influence of loading path change: Prediction strategy and model validation. Int J Mech Sci 183:105791. https://doi.org/10.1016/j.ijmecsci.2020.105791

    Article  Google Scholar 

  27. Tozawa Y (1978) Plastic deformation behavior under conditions of combined stress. In: Koistinen, D.P., Wang, NM. (eds) Mechanics of Sheet Metal Forming. Springer, pp 81–110

  28. Khan AS, Kazmi R, Pandey A, Stoughton T (2009) Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511). Int J Plast 25:1611–1625. https://doi.org/10.1016/j.ijplas.2008.07.003

    Article  Google Scholar 

  29. Khan AS, Pandey A, Stoughton T (2010) Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al). Int J Plast 26:1421–1431. https://doi.org/10.1016/j.ijplas.2009.07.008

    Article  MATH  Google Scholar 

  30. Zhu S, Zhuang X, Xu D et al (2019) Flange forming at an arbitrary tube location through upsetting with a controllable deformation zone. J Mater Process Technol 273:116230. https://doi.org/10.1016/j.jmatprotec.2019.05.011

    Article  Google Scholar 

  31. Simões VM, Oliveira MC, Neto DM et al (2018) Numerical study of springback using the split-ring test: influence of the clearance between the die and the punch. Int J Mater Form 11:325–337. https://doi.org/10.1007/s12289-017-1351-x

    Article  Google Scholar 

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (51875351) and Shanghai Outstanding Academic Leaders Plan (21XD1422000).

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Authors and Affiliations

  1. Institute of Forming Technology and Equipment, School of Materials Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Wen Zhang, Huachao Yang, Xincun Zhuang, Hongfei Wu & Zhen Zhao

  2. National Engineering Research Center of Die & Mold CAD, Shanghai Jiao Tong University, 200030, Shanghai, China

    Zhen Zhao

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  1. Wen Zhang
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  2. Huachao Yang
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Correspondence to Xincun Zhuang or Zhen Zhao.

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Zhang, W., Yang, H., Zhuang, X. et al. Comparative study of various hardening models for the prediction of plastic responses under strain path change conditions. Int J Mater Form 15, 38 (2022). https://doi.org/10.1007/s12289-022-01673-9

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