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Theoretical and Numerical Investigation of the Limit Strain of a 5754-O Aluminum Alloy Sheet Considering the Influence of the Hardening Law

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Abstract

This work focuses on the limit strains of 5754-O aluminum alloy sheets with consideration of the hardening law effect. Based on uniaxial tension test data, the hardening laws of Swift, Voce, LSV and Hockett–Sherby were applied to determine the mechanical properties. The fitted parameters and the Yld2000-2d yield function were introduced into the Marciniak–Kuczynski (M–K) theory to predict the forming limit curve (FLC). This prediction was not consistent with the Nakajima test results. Assessment of the effect of the hardening law on the predicted FLC indicated that the hardening law affected the yield surface evolution through the hardening rate. Afterward, an improved LSV hardening law was proposed to depict the plastic stress–strain relationship, and both the theoretical prediction and the numerical simulation verified the validity of the improved model. The results were compared with the test data, and good agreement was shown.

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References

  1. D.W.A. Rees, Factors influencing the FLD of automotive sheet metal [J], J. Mater. Process. Technol., 2001, 118(1–3), p 1–8.

    Article  Google Scholar 

  2. A. Graf and W. Hosford, The influence of strain-path changes on forming limit diagrams of A1 6111 T4 [J], Int. J. Mech. Sci., 1994, 36(10), p 897–910.

    Article  Google Scholar 

  3. R. Uppaluri, N.V. Reddy and P.M. Dixit, An analytical approach for the prediction of forming limit curves subjected to combined strain paths [J], Int. J. Mech. Sci., 2011, 53(5), p 365–373.

    Article  Google Scholar 

  4. J. Cao, H. Yao, A. Karafillis et al., Prediction of localized thinning in sheet metal using a general anisotropic yield criterion [J], Int. J. Plast, 2000, 16(9), p 1105–1129.

    Article  CAS  Google Scholar 

  5. A. Reyes, O.S. Hopperstad, T. Berstad et al., Prediction of necking for two aluminum alloys under non-proportional loading by using an FE-based approach [J], Int.J. Mater. Form., 2008, 1(4), p 211–232.

    Article  Google Scholar 

  6. D. Vysochinskiy, T. Coudert, O.S. Hopperstad et al., Experimental study on the formability of AA6016 sheets pre-strained by rolling [J], Int.J. Mater. Form., 2017, 10, p 1–17.

    Google Scholar 

  7. S. Dhara, S. Basak, S.K. Panda et al., Formability analysis of pre-strained AA5754-O sheet metal using Yld96 plasticity theory: role of amount and direction of uni-axial pre-strain [J], J. Manuf. Process., 2016, 24, p 270–282.

    Article  Google Scholar 

  8. H.J. Kleemola and M.T. Pelkkikangas, Effect of predeformation and strain path on the forming limits of steel [J], Sheet Metal Industries, 1977, 64(6), p 591–592.

    Google Scholar 

  9. G. Fang, Q.J. Liu, L.P. Lei et al., Comparative analysis between stress- and strain-based forming limit diagrams for aluminum alloy sheet 1060 [J], Trans. Nonferr. Metals Soc. China, 2012, 22(Suppl 2), p s343–s349.

    Article  CAS  Google Scholar 

  10. A. Werber, W. Nester, M. Gr Nbaum et al., Assessment of forming limit stress curves as failure criterion for non-proportional forming processes [J], Prod Eng Res Develop, 2013, 7(2–3), p 213–221.

    Article  Google Scholar 

  11. S.K. Paul, Path independent limiting criteria in sheet metal forming [J], J. Manuf. Process., 2015, 20, p 291–303.

    Article  Google Scholar 

  12. T.B. Stoughton and X. Zhu, Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD [J], Int. J. Plast, 2004, 20(8), p 1463–1486.

    Article  Google Scholar 

  13. H. Wang, Y. Yan, M. Wan et al., Experimental investigation and constitutive modeling for the hardening behavior of 5754O aluminum alloy sheet under two-stage loading [J], Int. J. Solids Struct., 2012, 49(26), p 3693–3710.

    Article  CAS  Google Scholar 

  14. P. Dasappa, K. Inal and R. Mishra, The effects of anisotropic yield functions and their material parameters on prediction of forming limit diagrams [J], Int. J. Solids Struct., 2012, 49(25), p 3528–3550.

    Article  CAS  Google Scholar 

  15. A.B.D. Rocha, A.D. Santos, P. Teixeira et al., Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming [J], J. Mater. Process. Technol., 2009, 209(11), p 5097–5109.

    Article  Google Scholar 

  16. F. Barlat, J.C. Brem, J.W. Yoon et al., Plane stress yield function for aluminum alloy sheets—part 1: theory [J], Int. J. Plast, 2003, 19(9), p 1297–1319.

    Article  CAS  Google Scholar 

  17. M.A. Iadicola, T. Foecke and S.W. Banovic, Experimental observations of evolving yield loci in biaxially strained AA5754-O [J], Int. J. Plast, 2008, 24(11), p 2084–2101.

    Article  CAS  Google Scholar 

  18. H. Wang, Y. Liu, Z. Chen et al., Investigation of the capabilities of yield functions on describing the deformation behavior of 5754O aluminum alloy sheet under combined loading paths [J], J Shanghai Jiaotong Univ (Sci), 2016, 21(5), p 562–568.

    Article  Google Scholar 

  19. H. Wang, M. Wan, X. Wu et al., The equivalent plastic strain-dependent Yld 2000–2d yield function and the experimental verification [J], Comput. Mater. Sci., 2009, 47(1), p 12–22.

    Article  CAS  Google Scholar 

  20. T. Kuwabara, T. Mori, M. Asano et al., Material modeling of 6016-O and 6016–T4 aluminum alloy sheets and application to hole expansion forming simulation [J], Int. J. Plasticity, 2016, 93, p 164.

    Article  Google Scholar 

  21. Q.T. Pham, B.H. Lee, K.C. Park et al., Influence of the post-necking prediction of hardening law on the theoretical forming limit curve of aluminium sheets [J], Int. J. Mech. Sci., 2018, 140, p 521.

    Article  Google Scholar 

  22. Q.T. Pham and Y.S. Kim, Identification of the plastic deformation characteristics of AL5052-O sheet based on the non-associated flow rule [J], Met. Mater. Int., 2017, 23, p 1–10.

    Article  Google Scholar 

  23. Z. Gronostajski, The constitutive equations for FEM analysis [J], J. Mater. Processi. Tech, 2000, 106(1), p 40–44.

    Article  Google Scholar 

  24. M.C. Butuc, J.J. Gracio and A.B.D. Rocha, A theoretical study on forming limit diagrams prediction [J], J. Mater. Process. Technol., 2003, 142(3), p 714–724.

    Article  CAS  Google Scholar 

  25. J. Ding, C. Zhang, X. Chu et al., Investigation of the influence of the initial groove angle in the M-K model on limit strains and forming limit curves [J], Int. J. Mech. Sci., 2015, 98, p 59–69.

    Article  Google Scholar 

  26. Z. Marciniak and K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal [J], Int. J. Mech. Sci., 1967, 9(9), p 609–620.

    Article  Google Scholar 

  27. B.L. Ma, M. Wan, X.J. Li et al., Evaluation of limit strain and temperature history in hot stamping of advanced high strength steels (AHSS) [J], Int. J. Mech. Sci., 2017, 129, p 607–613.

    Article  Google Scholar 

  28. B.L. Ma, M. Wan, X.D. Wu et al., Investigation on forming limit of advanced high strength steels (AHSS) under hot stamping conditions [J], J. Manuf. Process., 2017, 30, p 320–327.

    Article  Google Scholar 

  29. B. Ma, K. Diao, X. Wu et al., The effect of the through-thickness normal stress on sheet formability [J], J. Manuf. Process., 2016, 21, p 134–140.

    Article  Google Scholar 

  30. H. Aretz, A simple isotropic-distortional hardening model and its application in elastic–plastic analysis of localized necking in orthotropic sheet metals [J], Int. J. Plast, 2008, 24(9), p 1457–1480.

    Article  CAS  Google Scholar 

  31. K. Yoshida, T. Ishizaka, M. Kuroda et al., The effects of texture on formability of aluminum alloy sheets [J], Acta Mater., 2007, 55(13), p 4499–4506.

    Article  CAS  Google Scholar 

  32. R. Chiba, H. Takeuchi, M. Kuroda et al., Theoretical and experimental study of forming-limit strain of half-hard AA1100 aluminium alloy sheet [J], Comput. Mater. Sci., 2013, 77(3), p 61–71.

    Article  CAS  Google Scholar 

  33. H. Wang, Y. Yan, F. Han et al., Experimental and theoretical investigations of the forming limit of 5754O aluminum alloy sheet under different combined loading paths [J], Int. J. Mech. Sci., 2017, 133, p 147.

    Article  Google Scholar 

  34. Z.M. Yue, H. Badreddine, T. Dang et al., Formability prediction of AL7020 with experimental and numerical failure criteria [J], J. Mater. Process. Tech, 2015, 218, p 80–88.

    Article  CAS  Google Scholar 

  35. D. Banabic, H. Aretz, L. Paraianu et al., Application of various FLD modelling approaches [J], Modell. Simul. Mater. Sci. Eng., 2005, 13(5), p 759–769.

    Article  CAS  Google Scholar 

  36. X. Chu, L. Leotoing, D. Guines et al., Temperature and strain rate influence on AA5086 forming limit curves: experimental results and discussion on the validity of the M-K model [J], Int. J. Mech. Sci., 2014, 78(78), p 27–34.

    Article  Google Scholar 

  37. C. Zhang, L. Leotoing, G. Zhao et al., A methodology for evaluating sheet formability combining the tensile test with the M-K model [J], Mater. Sci. Eng., A, 2010, 528(1), p 480–485.

    Article  Google Scholar 

  38. W.N. Yuan, M. Wan, X.D. Wu et al., A numerical M-K approach for predicting the forming limits of material AA5754-O [J], Int. J. Adv. Manuf. Technol., 2018, 2, p 87. https://doi.org/10.1007/s00170-00018-02332-z

    Article  Google Scholar 

  39. B.L. Ma, M. Wan, Z.Y. Cai et al., Investigation on the forming limits of 5754-O aluminium alloy sheet with the numerical Marciniak-Kuczynski approach [J], Int. J. Mech. Sci., 2018, 142, p 25.

    Google Scholar 

  40. B.L. Ma, M. Wan, Z.G. Liu et al., Experimental and numerical determination of hot forming limit curve of advanced high-strength steel [J], J. Mater. Eng. Perform., 2017, 26(15), p 1–8.

    Google Scholar 

  41. F. Ozturka and D. Leeb, Experimental and numerical analysis of out-of-plane formability test [J], J. Mater. Process. Tech, 2005, 170(1), p 247–253.

    Article  Google Scholar 

  42. S. Zhang, L. Leotoing, D. Guines et al., Calibration of anisotropic yield criterion with conventional tests or biaxial test [J], Int. J. Mech. Sci., 2014, 85(1–4), p 142–151.

    Article  Google Scholar 

  43. O. Hering, F. Kolpak and A.E. Tekkaya, Flow curves up to high strains considering load reversal and damage[J], Int. J. Mater. Form., 2019, 12(32), p 955–972.

    Article  Google Scholar 

  44. J. Chen, Z. Guan, P. Ma, Z. Li and D. Gao, Experimental extrapolation of hardening curve for cylindrical specimens via pre-torsion tension tests, J. Strain Anal. Eng. Des., 2020, 55(1–2), p 20–30.

    Article  Google Scholar 

  45. H. Zhang, S. Coppieters, C. Jiménez-Peña et al., Inverse identification of the post-necking work hardening behaviour of thick HSS through full-field strain measurements during diffuse necking[J], Mech. Mater., 2018, 129(1), p 361.

    Google Scholar 

  46. J. Chen, Z. Guan, J. Xing et al., Methods for measuring friction-independent flow stress curve to large strains using hyperbolic shaped compression specimen, J. Strain Anal. Eng. Des., 2022, 57(1), p 23–37.

    Article  Google Scholar 

  47. Z. Cai, M. Wan, Z. Liu et al., Thermal-mechanical behaviors of dual-phase steel sheet under warm-forming conditions [J], Int. J. Mech. Sci., 2017, 126, p 79–94.

    Article  Google Scholar 

  48. B.L. Ma, M. Wan, H. Zhang et al., Evaluation of the forming limit curve of medium steel plate based on non-constant through-thickness normal stress [J], J. Manuf. Processes, 2018, 33, p 175–183.

    Article  Google Scholar 

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Acknowledgments

This study was supported by a grant from the National Natural Science Foundation of China (No. 52005516) and the Project of the State Key Laboratory of High Performance Complex Manufacturing, Central South University (Nos. ZZYJKT2021-03).

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Authors and Affiliations

  1. Light Alloy Research Institute, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Bolin Ma, Chunyu Yang & Lihua Zhan

  2. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, People’s Republic of China

    Xiangdong Wu

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Ma, B., Yang, C., Wu, X. et al. Theoretical and Numerical Investigation of the Limit Strain of a 5754-O Aluminum Alloy Sheet Considering the Influence of the Hardening Law. J. of Materi Eng and Perform 32, 10115–10127 (2023). https://doi.org/10.1007/s11665-023-07849-x

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