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Research on the thermal forming limit diagram (TFLD) with the M-K model for Ti-6Al-4V alloy

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Abstract

The formability of Ti-6Al-4V titanium alloy at high temperatures is critical in assisting the manufacture of aircraft components. The predicted forming limit curves (FLCs) of Ti-6Al-4V under elevated temperatures are mainly determined by the constitutive equation introduced into the M-K model. In the article, the thermal tensile test (650–750 °C, strain rate 0.1–0.001 s−1) was performed, and the relevant flow curve was fitted by the Backofen constitutive equation considering the variation of material parameters. The M-K model was established to predict the forming limit diagram (FLD) of Ti-6Al-4V alloy at various temperatures and strain rates based upon the Backofen model and Von Mises yield criterion, which was further verified by the hot Nakajima-type bulging experiment. The bulging experiment was also conducted by the finite element method (FEM) to obtain the limit dome height (LDH) at various temperatures under the strain rate of 0.1s−1. Moreover, the internal forming mechanism of Ti-6Al-4V alloy with strain rate and temperature was analyzed from the micro-perspective. The contrast of experimental and simulation results indicated that the formability of the alloy increased with increasing temperature and decreasing strain rate. The M-K model utilizing the Backofen model conduces to the accurate thermal forming limit diagram (TFLD) prediction of Ti-6Al-4V.

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References

  1. Cai J, Li FG, Liu TY, Chen B, He M (2011) Constitutive equations for elevated temperature flow stress of Ti–6Al–4V alloy considering the effect of strain. Mater Des 32(3):1144–1151. https://doi.org/10.1016/j.matdes.2010.11.004

    Article  Google Scholar 

  2. Seshacharyulu T, Medeiros SC, Frazier WG, Prasad YVRK (2000) Hot working of commercial Ti–6Al–4V with an equiaxed α–β microstructure: materials modeling considerations. Mater Sci Eng A 284(1-2):184–194. https://doi.org/10.1016/S0921-5093(00)00741-3

    Article  Google Scholar 

  3. Vanderhasten M, Rabet L, Verlinden B (2007) Deformation mechanisms of Ti-6Al-4V during tensile behavior at low strain rate. J Mater Eng Perform 16(2):208–212. https://doi.org/10.1007/s11665-007-9033-3

    Article  Google Scholar 

  4. Gorynin IV (1999) Titanium alloys for marine application. Mater Sci Eng A 263(2):112–116. https://doi.org/10.1016/S0921-5093(98)01180-0

    Article  Google Scholar 

  5. Bruschi S, Poggio S, Quadrini F, Tata ME (2004) Workability of Ti–6Al–4V alloy at high temperatures and strain rates. Mater Lett 58(27-28):3622–3629. https://doi.org/10.1016/j.matlet.2004.06.058

    Article  Google Scholar 

  6. Xiao J, Li DS, Li XQ, Deng TS (2012) Constitutive modeling and microstructure change of Ti–6Al–4V during the hot tensile deformation. J Alloys Compd 541:346–352. https://doi.org/10.1016/j.jallcom.2012.07.048

    Article  Google Scholar 

  7. Vanderhasten M, Rabet L, Verlinden B (2008) Ti–6Al–4V: Deformation map and modelization of tensile behavior. Mater Des 29(6):1090–1098. https://doi.org/10.1016/j.matdes.2007.06.005

    Article  Google Scholar 

  8. Yao H, Cao J (2002) Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress. Int J Plast 18(8):1013–1038. https://doi.org/10.1016/S0749-6419(01)00022-5

    Article  Google Scholar 

  9. Fan GQ, Sun FT, Meng XG, Gao L, Tong GQ (2010) Electric hot incremental forming of Ti-6Al-4V titanium sheet. Int J Adv Manuf Technol 49(9):941–947. https://doi.org/10.1007/s00170-009-2472-2

    Article  Google Scholar 

  10. Lai CP, Chan LC, Chou CL, Yu KM (2010) Thermal forming of light-weight alloys under a multi-stage forming process. Proc Inst Mech Eng C J Mech Eng Sci 224(4). https://doi.org/10.1243/09544062JMES1456

  11. Zhang CS, Leotoing L, Guines D, Ragneau E (2009) Theoretical and numerical study of strain rate influence on AA5083 formability. J Mater Process Technol 209:3849–3858. https://doi.org/10.1016/j.jmatprotec.2008.09.003

    Article  Google Scholar 

  12. Panich S, Barlat F, Uthaisangsuk V, Suranuntchai S, Jirathearanat S (2013) Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels. Mater Des 51:756–766. https://doi.org/10.1016/j.matdes.2013.04.080

    Article  Google Scholar 

  13. Ahmadi S, Eivani AR, Akbarzadeh A (2009) An experimental and theoretical study on the prediction of forming limit diagrams using new BBC yield criteria and M–K analysis. Comput Mater Sci 44(4):1272–1280. https://doi.org/10.1016/j.commatsci.2008.08.013

    Article  Google Scholar 

  14. Dong GJ, Chen ZW, Yang ZY, Fan BC (2020) Comparative study on forming limit prediction of AA7075-T6 sheet with MK model and LouHuh criterion. Trans Nonferrous Met Soc 30(6):1463–1477. https://doi.org/10.1016/S1003-6326(20)65311-0

    Article  Google Scholar 

  15. Ding J, Zhang CS, Chu XR, Zhao GQ, Leotoing L, Guines D (2015) Investigation of the influence of the initial groove angle in the M-K model on limit strains and forming limit curves. Int J Mech Sci 98:59–69. https://doi.org/10.1016/j.ijmecsci.2015.04.011

    Article  Google Scholar 

  16. Kotkunde N, Srinivasan S, Krishna G, Gupta AK, Singh SK (2016) Influence of material models on theoretical forming limit diagram prediction for Ti-6Al-4V alloy under warm condition. Trans Nonferrous Met Soc 26(3):736–746. https://doi.org/10.1016/S1003-6326(16)64140-7

    Article  Google Scholar 

  17. 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 Plastic 5(1):51–66. https://doi.org/10.1016/0749-6419(89)90019-3

  18. Hill R (1993) A user-friendly theory of orthotropic plasticity in sheet metals. Int J Mech Sci 35(1):19–25. https://doi.org/10.1016/0020-7403(93)90061-X

  19. Li XQ, Guo GQ, Xiao JJ, Song N, Li DS (2014) Constitutive modeling and the effects of strain-rate and temperature on the formability of Ti–6Al–4V alloy sheet. Mater Des 55(1):325–334. https://doi.org/10.1016/j.matdes.2013.09.069

    Article  Google Scholar 

  20. Ma BL, Wu XD, Li XJ, Wan M, Cai ZY (2016) Investigation on the hot formability of TA15 titanium alloy sheet. Mater Des 94:9–16. https://doi.org/10.1016/j.matdes.2016.01.010

    Article  Google Scholar 

  21. Wu Y, Liu G, Liu ZQ, Wang B (2016) Formability and microstructure of Ti22Al24.5Nb0.5Mo rolled sheet within hot gas bulging tests at constant equivalent strain rate. Mater Des 108:298–307. https://doi.org/10.1016/j.matdes.2016.06.109

    Article  Google Scholar 

  22. Fan RL, Chen MH, Wu Y, Xie LS (2018) Prediction and experiment of fracture behavior in hot press forming of a TA32 titanium alloy rolled sheet. Metals 8(12):985. https://doi.org/10.3390/met8120985

    Article  Google Scholar 

  23. Bong HJ, Yoo DH, Kim D, Kwon YN, Lee J (2020) Correlative study on plastic response and formability of Ti-6Al-4V sheets under hot forming conditions. J Manuf Process 58:775–786. https://doi.org/10.1016/j.jmapro.2020.08.053

    Article  Google Scholar 

  24. Kotkunde N, Gupta AK (2015) Analysis of forming limit diagram for Ti-6Al-4V alloy. Mater Today Proc 2(4-5):3762–3769. https://doi.org/10.1016/j.matpr.2015.07.178

    Article  Google Scholar 

  25. Zhang HB, Zhang KF, Zhou HP, Lu Z, Zhao CH (2015) Effect of strain rate on microstructure evolution of a nickel-based superalloy during hot deformation. Mater Des 80:51–62. https://doi.org/10.1016/j.matdes.2015.05.004

    Article  Google Scholar 

  26. Ying L, Gao TH, Rong H, Han X, Hu P, Hou WB (2019) On the thermal forming limit diagram (TFLD) with GTN mesoscopic damage model for AA7075 aluminum alloy: numerical and experimental investigation. J Alloys Compd 802:675–693. https://doi.org/10.1016/j.jallcom.2019.05.342

    Article  Google Scholar 

  27. Chong Y, Bhattacharjee T, Gholizadeh R, Yi JH, Tshji N (2019) Investigation on the hot deformation behaviors and globularization mechanisms of lamellar Ti–6Al–4V alloy within a wide range of deformation temperatures. Materialia 8:100480. https://doi.org/10.1016/j.mtla.2019.100480

    Article  Google Scholar 

  28. Zaiemyekeh Z, Liaghat GH, Ahmadi H, Khan MK, Razmkhah O (2019) Effect of strain rate on deformation behavior of aluminum matrix composites with Al2O3 nanoparticles. Mater Sci Eng A 753:276–284. https://doi.org/10.1016/j.msea.2019.03.052

    Article  Google Scholar 

  29. Dayananda GN, Rao MS (2008) Effect of strain rate on properties of superelastic NiTi thin wires. Mater Sci Eng A 486(1-2):96–103. https://doi.org/10.1016/j.msea.2007.09.006

    Article  Google Scholar 

  30. Zheng ZB, Waheed S, Balint DS, Dunne FPE (2018) Slip transfer across phase boundaries in dual phase titanium alloys and the effect on strain rate sensitivity. Int J Plast 104:23–38. https://doi.org/10.1016/j.ijplas.2018.01.011

    Article  Google Scholar 

  31. Gao S, He TG, Li QH, Sun YL, Sang Y, Wu YH, Ying L (2022) Anisotropic behavior and mechanical properties of Ti-6Al-4V alloy in high temperature deformation. J Mater Sci 57(1):651–670. https://doi.org/10.1007/s10853-021-06569-8

    Article  Google Scholar 

  32. Naka T, Totikai G, Hino R, Yoshida F (2001) The effects of temperature and forming speed on the forming limit diagram for type 5083 aluminum-magnesium alloy sheet. J Mater Process Technol 113(1):648–653. https://doi.org/10.1016/S0924-0136(01)00650-1

    Article  Google Scholar 

  33. Soare SC (2010) Theoretical considerations upon the MK model for limit strains prediction: the plane strain case, strain-rate effects, yield surface influence, and material heterogeneity. J Mech A Solids 29(6):938–950. https://doi.org/10.1016/j.euromechsol.2010.05.008

    Article  Google Scholar 

  34. Heigel JC, Michaleris P, Reutzel EW (2015) Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of Ti–6Al–4V. Addit Manuf 5:9–19. https://doi.org/10.1016/j.addma.2014.10.003

    Article  Google Scholar 

  35. Welsch G, Boyer R, Collings EW (1993) Materials properties handbook: titanium alloys. ASM international

    Google Scholar 

  36. Yu CC (2020) Numerical research of multi-point 3D hot stretch-bending process for titanium alloy profiles. Dissertation, Changchun university of technology

    Google Scholar 

  37. Yoo MH, Morris JR, Ho KM, Agnew SR (2002) Nonbasal deformation modes of HCP metals and alloys: role of dislocation source and mobility. Metall Mater Trans A 33(13):813–822. https://doi.org/10.1007/s11661-002-0150-1

    Article  Google Scholar 

  38. Hémery S, Villechaise P, Banerjee D (2020) Microplasticity at room temperature in α/β titanium alloys. Metall Mater Trans A 51(10):4931–4969. https://doi.org/10.1007/s11661-020-05945-4

    Article  Google Scholar 

  39. Stapleton AM, Raghunathan SL, Bantounas I, Stone HJ, Lindley TC, Dye D (2008) Evolution of lattice strain in Ti–6Al–4V during tensile loading at room temperature. Acta Mater 56(20):6186–6196. https://doi.org/10.1016/j.actamat.2008.08.030

    Article  Google Scholar 

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Data and code availability

Due to the sensitive nature of the questions asked in this study, survey respondents were assured raw data would remain confidential and would not be shared.

Funding

This work was supported by the National Natural Science Foundation of China (no.51805045) and the Scientific and Technological Developing Scheme of Ji Lin Province (no. 20210201052GX) and (no. 20230508115RC).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Changchun University of Technology, Changchun, 130012, Jilin, China

    Song Gao, Guotao Wang, Ye Sang, Yingli Sun & Qihan Li

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Contributions

Song Gao: methodology, writing—reviewing and editing, and project administration. Guotao Wang: data curation and writing—original draft preparation. Ye Sang: software, visualization, and investigation. Yingli Sun: supervision and conceptualization. Qihan Li: investigation and project administration.

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Correspondence to Song Gao or Guotao Wang.

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Gao, S., Wang, G., Sang, Y. et al. Research on the thermal forming limit diagram (TFLD) with the M-K model for Ti-6Al-4V alloy. Int J Adv Manuf Technol 131, 3713–3728 (2024). https://doi.org/10.1007/s00170-024-13154-1

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