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A comparison study of the yield surface exponent of the Barlat yield function on the forming limit curve prediction of zirconium alloys with M-K method

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Abstract

The forming limit curve (FLC) of zirconium alloys plays a significant role in the fabrications of spacer grid used for nuclear fuel assembly. The theoretical prediction of FLC has provided a convenient method to calculate the strain limit during the sheet forming process, but the prediction accuracy of zirconium alloy is still unsatisfactory due to its close-packed-hexagonal (HCP) structure. In this paper, to find a suitable yield surface exponent of zirconium alloys for improving the prediction accuracy, the theoretical FLCs of SZA6 zirconium alloy were calculated by self-programmed numerical codes with different exponent values and the results were compared with the experiments. To explain the mechanism of how the yield surface exponent affects the plastic behavior of SZA6 zirconium alloy, the strain distributions and element strain paths of Nakajima test were analyzed by finite element methods. At last, a suggested value of the yield surface exponent suitable for the FLC prediction of this zirconium alloy is acquired.

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References

  1. Vasnin AM, Gol'tsev VY, Markochev VM, Rivkin EY (1975) Resistance to fracture of a zirconium alloy containing 2.5% Nb. Strength Mater 6(12):1535–1539

    Article  Google Scholar 

  2. Kolesnik M, Aliev T, Likhanskii V (2019) The modeling of the hydrogen solid solubility hysteresis in zirconium alloys. Acta Mater 177:131–140. https://doi.org/10.1016/j.actamat.2019.07.044

    Article  Google Scholar 

  3. Jung Y-I, Lee M-H, Choi B-K, Park J-Y, Jeong Y-H (2009) Development of a manufacturing process for Zr-based spacer grid materials. J Nucl Mater 392(3):482–486. https://doi.org/10.1016/j.jnucmat.2009.04.012

    Article  Google Scholar 

  4. Chen J, Hu Q, Lv X, Li X (2017) Numerical simulation and experiment study on the nuclear fuel spacer grid stamping of Inconel 718. Procedia Eng 207:1534–1539

    Article  Google Scholar 

  5. Kim M, Rickhey F, Lee H, Kim N (2016) Analytical determination of forming limit curve for zirlo and its experimental validation. J Manuf Process 23:122–129. https://doi.org/10.1016/j.jmapro.2016.06.006

    Article  Google Scholar 

  6. Gensamer M (2017) Strength and ductility. Metallogr Microstruct Anal 6(2):171–185

    Article  Google Scholar 

  7. Banabic D, Kami A, Comsa D-S, Eyckens P (2021) Developments of the Marciniak-Kuczynski model for sheet metal formability: A review. J Mater Process Technol 287:116446. https://doi.org/10.1016/j.jmatprotec.2019.116446

    Article  Google Scholar 

  8. Keeler SP (1961) Plastic instability and fracture in sheets stretched over rigid punches. Doctoral dissertation, Massachusetts Institute of Technology

    Google Scholar 

  9. Keeler SP (1965) Determination of Forming Limits in Automotive Stampings (No. 650535). SAE Technical Paper. https://doi.org/10.4271/650535

  10. Goodwin GM (1968) Application of strain analysis to sheet metal forming problems in the press shop. SAE Trans:380–387. https://doi.org/10.4271/680093

  11. Dizaji SA, Darendeliler H, Kaftanoğlu B (2018) Prediction of forming limit curve at fracture for sheet metal using new ductile fracture criterion. Eur J Mech- A/Solids 69:255–265

    Article  MathSciNet  Google Scholar 

  12. Ma B, Liu ZG, Jiang Z, Wu X, Diao K, Wan M (2016) Prediction of forming limit in DP590 steel sheet forming: an extended fracture criterion. Mater Des 96:401–408

    Article  Google Scholar 

  13. Considère M (1885) L’emploi du fer et l’acier dans les constructions. Ann des Ponts et Chausses 9:574–775

    Google Scholar 

  14. Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1(1):1–18

    Article  MathSciNet  Google Scholar 

  15. Hill R (1952) On discontinuous plastic states, with special reference to localized necking in thin sheets. J Mech Phys Solids 1(1):19–30

    Article  MathSciNet  Google Scholar 

  16. D. Banabic, Multiscale Modelling in sheet metal forming, 2016

    Book  Google Scholar 

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

    Article  Google Scholar 

  18. Cheng C, Wan M, Wu XD, Cai ZY, Zhao R, Meng B (2017) Effect of yield criteria on the formability prediction of dual-phase steel sheets. Int J Mech Sci 133:28–41. https://doi.org/10.1016/j.ijmecsci.2017.08.033

    Article  Google Scholar 

  19. Hill RA Theory of the Yielding and Plastic Flow of Anisotropic Metals. Proc R Soc Lond 193(1033):281–297. https://doi.org/10.1098/rspa.1948.0045 Published 27 May 1948

  20. Yan Y, Wang H, Li Q (2015) The inverse parameter identification of Hill 48 yield criterion and its verification in press bending and roll forming process simulations. J Manuf Process 20:46–53. https://doi.org/10.1016/j.jmapro.2015.09.009

    Article  Google Scholar 

  21. Nurcheshmeh M, Green DE (2016) Prediction of forming limit curves for nonlinear loading paths using quadratic and non-quadratic yield criteria and variable imperfection factor. Mater Des 91:248–255. https://doi.org/10.1016/j.matdes.2015.11.098

    Article  Google Scholar 

  22. Hill R (1979) Theoretical plasticity of textured aggregates. Math Proc Camb Philos Soc 85(1):179–191. https://doi.org/10.1017/S0305004100055596

    Article  MathSciNet  MATH  Google Scholar 

  23. Hosford WF (1985) Comments on anisotropic yield criteria. Int J Mech Sci 27(7):423–427

    Article  Google Scholar 

  24. Hosford WF (1979) On yield loci of anisotropic cubic metals. In: Proceedings of the Seventh North American Metal working Conference SME, pp 191–197

    Google Scholar 

  25. Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech 39(2):607–609

    Article  Google Scholar 

  26. 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 Plasticity 5(1):51–66

    Article  Google Scholar 

  27. Hill R (1993) A user-friendly theory of orthotropic plasticity in sheet metals. Int J Mech Sci 35(1):19–25

    Article  Google Scholar 

  28. Banabic D (2010) Sheet metal forming processes. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  29. Hu G, Cai X, Rong Y (2010) Fundamentals of Materials Science. Jiao Tong University Press, Shanghai

    Google Scholar 

  30. Vial-Edwards C (1997) Yield loci of FCC and BCC sheet metals. Int J Plast 13(5):521–531

    Article  Google Scholar 

  31. Cazacu O, Barlat F (2001) Generalization of Drucker's yield criterion to Orthotropy. Math Mech Solids 6(6):613–630

    Article  Google Scholar 

  32. Cazacu O, Barlat F (2003) Application of the theory of representation to describe yielding of anisotropic aluminum alloys. Int J Eng Sci 41(12):1367–1385

    Article  Google Scholar 

  33. Cazacu O, Barlat F (2004) A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals. Int J Plast 20(11):2027–2045

    Article  Google Scholar 

  34. Banabic D, Kuwabara T, Balan T, Comsa DS, Julean D (2003) A new yield criterion for orthotropic sheet metals under plane-stress conditions. Int J Mech ences 45(5):797–811

    Article  Google Scholar 

  35. Banabic D, Aretz H, Comsa DS, Paraianu L (2005) An improved analytical description of orthotropy in metallic sheets. Int J Plast 21(3):493–512

    Article  Google Scholar 

  36. Liu C, Huang Y, Stout MG (1997) On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study. Acta Mater 45(6):2397–2406

    Article  Google Scholar 

  37. Pilthammar J, Banabic D, Sigvant M (2020) BBC05 with non-integer exponent and ambiguities in Nakajima yield surface calibration. Int J Mater Form. https://doi.org/10.1007/s12289-020-01545-0

  38. Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal closed packed metals. Int J Plast 22(7):1171–1194

    Article  Google Scholar 

  39. Plunkett B, Lebensohn RA, Cazacu O, Barlat F (2006) Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening. Acta Mater 54(16):4159–4169

    Article  Google Scholar 

  40. Hutchinson JW, Neale KW, N. A (1978) Sheet Necking—I. Validity of Plane Stress Assumptions of the Long-Wavelength Approximation. In: Koistinen DP, Wang NM (eds) Mechanics of Sheet Metal Forming Plenum, pp 111–126

    Chapter  Google Scholar 

  41. Hutchinson JW, N. KW (1978) Sheet Necking-II. Time-Independent Behavior. In: Koistinen DP, Wang NM (eds) Mechanics of Sheet Metal Forming Plenum, pp 127–153

    Chapter  Google Scholar 

  42. Hu Q, Li X, Chen J (2018) New robust algorithms for Marciniak–Kuczynski model to calculate the forming limit diagrams. Int J Mech Sci 148:293–306

    Article  Google Scholar 

  43. Backofen WA (1973) Deformation processing. Metall Trans A 4(12):2679–2699

    Article  Google Scholar 

  44. Hosford WF, Caddell RM (2011) Metal forming: mechanics and metallurgy. Cambridge University Press. https://doi.org/10.1017/CBO9780511811111

  45. Le C, Zhongbo Y, Jun Q, Bo L, Weijun L, Xiaofeng H, Lian W (2017) Effect of heat treatment on tensile properties and microstructure of new domestic zirconium alloys. Nuclear Power Eng 38(06):129–133

    Google Scholar 

  46. ASTM E8/E8M-16a Standard Test Methods for Tension Testing of Metallic Materials. (Published year: 2016)

  47. Morrison WB (1968) Superplasticity of low-alloy steels. ASM-Trans 61:423–434

    Google Scholar 

  48. International Standard ISO 12004–2, metallic materilas-sheet and strip-determinations of forming limit curves-part 2: determinations of forming limit curves in laboratory (2008)

    Google Scholar 

  49. Barlat F (1987) Crystallographic texture, anisotropic yield surfaces and forming limits of sheet metals. Mater Sci Eng A 91:55–72

    Article  Google Scholar 

  50. Ma BL, Wan M, Zhang H, Gong XL, Wu XD (2018) Evaluation of the forming limit curve of medium steel plate based on non-constant through-thickness normal stress. J Manuf Process 33:175–183

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Changsha, 410082, People’s Republic of China

    Congyi Lei, Jianzhong Mao, Xiaomin Zhang, Jingxuan Liu & Ding Chen

  2. College of Mechanical and Vehicle Engineer, Hunan University, Changsha, 410082, People’s Republic of China

    Congyi Lei, Jianzhong Mao, Xiaomin Zhang, Jingxuan Liu & Ding Chen

  3. State Nuclear Bao-Ti Zirconium Industry Company, Baoji, 721000, Shaanxi, China

    Lian Wang

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  1. Congyi Lei
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Lei, C., Mao, J., Zhang, X. et al. A comparison study of the yield surface exponent of the Barlat yield function on the forming limit curve prediction of zirconium alloys with M-K method. Int J Mater Form 14, 467–484 (2021). https://doi.org/10.1007/s12289-021-01616-w

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