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Finite element modeling for deep-drawing of aluminum alloy sheet 6014-T4 using anisotropic yield and non-AFR models

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Abstract

The predictive capability of a non-associated flow rule (non-AFR) for the strong plastic anisotropy was assessed. Based on Hill’s 48 function, a constitutive model under a non-AFR was established for aluminum alloy 6014-T4 sheet, in which the plastic potential function and the yield function were identified by Lankford coefficients (r-values) and yield stresses, respectively. Two constitutive models applying Hill’s 48 and Yld2000 functions under the AFR were also established for the comparison with the non-AFR Hill’s 48 model. These constitutive models were numerically carried out on Abaqus/Explicit by user subroutine (VUMAT). The representational ability of constitutive models was assessed in terms of the predictions on yield stresses and r-values. To further verify the simulated results, deep-drawing experiments of a cylindrical cup and a seat pan were performed. Simulation results were compared with the experiments from the aspects of the forming force, the earing profile, and the measured strain field using ex situ 3D DIC (Digital Image Correlation). Comparison results showed that non-AFR Hill’s 48 model gives the best overall prediction performance and requires less effort than the AFR Yld2000 model, indicating the effectiveness and superiority of non-AFR.

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References

  1. Bridgman PW (1947) The effect of hydrostatic pressure on the fracture of brittle substances. J Appl Phys 18(2):246–258

    Article  Google Scholar 

  2. Bridgman PW (1952) Studies in large plastic flow and fracture. McGraw-Hill, New York

    MATH  Google Scholar 

  3. Cvitanić V, Vlak F, Lozina Ž (2008) A finite element formulation based on non-associated plasticity for sheet metal forming. Int J Plast 24(4):646–687

    Article  MATH  Google Scholar 

  4. Maeda Y, Yanagawa M, Barlat F (1998) Experimental analysis of aluminum yield surface for binary Al Mg alloy sheet samples. Int J Plast 14(4–5):301–318

    Article  Google Scholar 

  5. Spitzig WA, Sober RJ, Richmond (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall Trans A 7(11):1703–1710

    Article  Google Scholar 

  6. Spitzig WA (1979) Effect of hydrostatic pressure on plastic-flow properties of iron single crystals. Acta Metall 27(4):523–534

    Article  Google Scholar 

  7. Spitzig WA, Richmond O (1984) The effect of pressure on the flow stress of metals. Acta Metall 32(3):457–463

    Article  Google Scholar 

  8. Bishop JFW, Hill R (1951) XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. London, Edinburgh, Dublin Philos Mag J Sci 42(327):414–427

    Article  MATH  Google Scholar 

  9. Li M, Richmond O (1997) Intrinsic instability and nonuniformity of plastic deformation. Int J Plast 13(8–9):765–784

    Article  MATH  Google Scholar 

  10. Stoughton TB (2002) A non-associated flow rule for sheet metal forming. Int J Plast 18(5–6):687–714

    Article  MATH  Google Scholar 

  11. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A 193(1033):281–297

    Article  MathSciNet  MATH  Google Scholar 

  12. Barlat F, Lian K (1989) Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int J Plast 5(1):51–66

    Article  Google Scholar 

  13. Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7(7):693–712

    Article  Google Scholar 

  14. Barlat F, Maeda Y, Chung K (1997) Yield function development for aluminum alloy sheets. J Mech Phys Solids 45:1727–1763

    Article  Google Scholar 

  15. Barlat F, Brem JC, Yoon JW (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19(9):1297–1319

    Article  MATH  Google Scholar 

  16. Barlat F, Aretz H, Yoon JW (2005) Linear transformation-based anisotropic yield functions. Int J Plast 21(5):1009–1039

    Article  MATH  Google Scholar 

  17. Esmaeilpour R, Kim H, Park T, Pourboghrat F, Mohammed B (2017) Comparison of 3D yield functions for finite element simulation of single point incremental forming (SPIF) of aluminum 7075. Int J Mech Sci 133:544–554

    Article  Google Scholar 

  18. Esmaeilpour R, Kim H, Park T, Pourboghrat F, Xu Z, Mohammed B, Abu-Farha F (2018) Calibration of Barlat Yld2004-18P yield function using CPFEM and 3D RVE for the simulation of single point incremental forming (SPIF) of 7075-O aluminum sheet. Int J Mech Sci 145:24–41

    Article  Google Scholar 

  19. Stoughton TB, Yoon JW (2004) A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming. Int J Plast 20(4–5):705–731

    Article  MATH  Google Scholar 

  20. Taherizadeh A, Green DE, Ghaei A, Yoon JW (2010) A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming. Int J Plast 26(2):288–309

    Article  MATH  Google Scholar 

  21. Park T, Chung K (2012) Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup deep-drawing. Int J Solids Struct 49(25):3582–3593

    Article  Google Scholar 

  22. Safaei M, Zang S, Lee MG, De Waele W (2013) Evaluation of anisotropic constitutive models: mixed anisotropic hardening and non-associated flow rule approach. Int J Mech Sci 73:53–68

    Article  Google Scholar 

  23. Safaei M, Yoon JW, De Waele W (2014) Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation. Int J Plast 58:219–238

    Article  Google Scholar 

  24. Manopulo N, List J, Gorji M (2015) A non-associated flow rule based yld2000-2d model//8th Forming Technology Forum Zurich

  25. Wu B, Ito K, Mori N, Oya T, Taylor T, Yanagimoto J (2019) Constitutive equations based on non-associated flow rule for the analysis of forming of anisotropic sheet metals. Int J Precis Eng Manuf Green Technol 1-16

  26. Paulino M, Yoon JW (2015) Study on yield function and plastic potential under non-associated flow for accurate earing prediction in cup drawing. Steel Res Int 86(8):852–860

    Article  Google Scholar 

  27. Prates PA, Oliveira MC, Fernandes JV (2016) Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy. Int J Mater Form 9(4):547–571

    Article  Google Scholar 

  28. Prates PA, Oliveira MC, Fernandes JV (2014) A new strategy for the simultaneous identification of constitutive laws parameters of metal sheets using a single test. Comput Mater Sci 85:102–120

    Article  Google Scholar 

  29. Dunand M, Maertens AP, Luo M, Mohr D (2012) Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading–part I: plasticity. Int J Plast 36:34–49

    Article  Google Scholar 

  30. Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming< 111>-pencil glide. Int J Mech Sci 22(7):419–430

    Article  Google Scholar 

  31. Qian LY, Fang G, Zeng P (2017) Modeling of the ductile fracture during the sheet forming of aluminum alloy considering non-associated constitutive characteristic. Int J Mech Sci 126:55–66

    Article  Google Scholar 

  32. Aretz H (2004) Applications of a new plane stress yield function to orthotropic steel and aluminium sheet metals. Model Simul Mater Sci Eng 12(3):491–509

    Article  Google Scholar 

  33. Chen Z, Fang G, Zhao JQ (2017) Formability evaluation of aluminum alloy 6061-T6 sheet at room and elevated temperatures. J Mater Eng Perform 26(9):4626–4637

    Article  Google Scholar 

  34. “Standard test method for tensile strain-hardening exponents (n-values) of metallic sheet materials,” ASTM E646–07, ASTM International, 2007

  35. Wang H, Wan M, Wu X, Yan Y (2009) The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification. Comput Mater Sci 47(1):12–22

    Article  Google Scholar 

  36. Deng Z, Hennig R (2017) Influence of material modeling on simulation accuracy of aluminum stampings. J Phys Conf Ser. IOP Publishing 896(1):012025

  37. Chen Z, Fang G (2018) Determination of forming limit for aluminium alloy sheet eliminating the interferences of through-thickness stress and non-linear strain path. IOP Conference Series: Materials Science and Engineering. IOP Publishing 418(1):012051

  38. Reu PL (2013) A study of the influence of calibration uncertainty on the global uncertainty for digital image correlation using a Monte Carlo approach. Exp Mech 53(9):1661–1680

    Article  Google Scholar 

  39. Chen F, Chen X, Xie X, Feng X, Yang L (2013) Full-field 3D measurement using multi-camera digital image correlation system. Opt Lasers Eng 51(9):1044–1052

    Article  Google Scholar 

  40. Tang Z, Liang J, Xiao Z, Guo C (2012) Large deformation measurement scheme for 3D digital image correlation method. Opt Lasers Eng 50(2):122–130

    Article  Google Scholar 

  41. Pan B, Xie H, Yang L, Wang Z (2009) Accurate measurement of satellite antenna surface using 3D digital image correlation technique. Strain 45(2):194–200

    Article  Google Scholar 

Download references

Acknowledgments

Prof. Haibo Wang of the North China University of Technology helped conduct equal biaxial tension tests. The author would like to express our thanks to these supports and helps.

Funding

The present study is financially supported by National Natural Science Foundation of China (No. 51705279 and No. 51375256).

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Correspondence to Gang Fang.

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Chen, Z., Zhao, J. & Fang, G. Finite element modeling for deep-drawing of aluminum alloy sheet 6014-T4 using anisotropic yield and non-AFR models. Int J Adv Manuf Technol 104, 535–549 (2019). https://doi.org/10.1007/s00170-019-03921-w

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