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A physically based constitutive model of Ti-6Al-4 V and application in the SPF/DB process for a pyramid lattice sandwich panel

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Abstract

The physically based constitutive modeling, simulation and experimental of a superplastic forming and diffusion bonding (SPF/DB) process were studied for the manufacture of a pyramid lattice Ti-6Al-4 V sandwich panel structure. The high-temperature deformation behaviors of Ti-6Al-4 V were studied using uniaxial tensile tests at various temperatures 860  – 950 °C and strain rates 0.0001 s−1 ~ 0.01 s−1, corresponding microstructures were observed using optical microscope (OM) and Electron Backscattered Diffraction (EBSD). Based on obtained flow behavior and microstructure, a set of physically based constitutive equations of the Ti-6Al-4 V was established and used to simulate the superplastic forming for a pyramid lattice sandwich panel. The thinning ratios, dislocation densities, grain sizes and damage distributions of the sandwich panels were successfully predicted by the finite element (FE) simulation. A pyramid lattice Ti-6Al-4 V alloy sandwich panel with good dimensional accuracy and mechanical properties was manufactured by the SPF/DB process at 920 °C with a gas loading path of 0.0005 MPa/s. The maximum thickness thinning ratio, damage factor and relative grain size at the ribs of the sandwich panel were 26.3%, 6.7% and 0.94, respectively. The established constitutive model aids the FE simulations of SPF/DB manufacture of sandwich panels’ structure enabling both macro- and micro-properties to be synergistically controlled and guides the practical process optimizations.

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References

  1. Banhart J. Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci. 2001;46(6):559–632.

    Article  Google Scholar 

  2. Evans AG, Hutchinson JW, Fleck NA, et al. The topological design of multifunctional cellular metals. Prog Mater Sci. 2001;46(3):309–27.

    Article  Google Scholar 

  3. Kim T, Hodson HP, Lu TJ. Fluid-flow and endwall heat-transfer characteristics of an ultralight lattice-frame material. Int J Heat Mass Transf. 2004;47(6–7):1129–40.

    Article  Google Scholar 

  4. Lu TJ, Hess A, Ashby M. Sound absorption in metallic foams. J Appl Phys. 1999;85(11):7528–39.

    Article  ADS  Google Scholar 

  5. Xue Z, Hutchinson JW. Preliminary assessment of sandwich plates subject to blast loads. Int J Mech Sci. 2003;45(4):687–705.

    Article  Google Scholar 

  6. Park K, Lee S, Kim C, et al. Fabrication and electromagnetic characteristics of electromagnetic wave absorbing sandwich structures. Compos Sci Technol. 2006;66(3):576–84.

    Article  Google Scholar 

  7. Wieding J, Jonitz A, Bader R. The effect of structural design on mechanical properties and cellular response of additive manufactured titanium scaffolds. Materials. 2012;5(8):1336–47.

    Article  ADS  Google Scholar 

  8. Liu Z, Chen H, Xing S. Mechanical performances of metal-polymer sandwich structures with 3D-printed lattice cores subjected to bending load. Arch Civil Mech Eng. 2020;20(3):89.

    Article  Google Scholar 

  9. Wadley HNG. Multifunctional periodic cellular metals. Philos Trans. 1838;2006(364):31–68.

    Google Scholar 

  10. Kooistra G. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. Acta Mater. 2004;52(14):4229–37.

    Article  ADS  Google Scholar 

  11. Tan Z, Bai L, Bai B, et al. Fabrication of lattice truss structures by novel super-plastic forming and diffusion bonding process in a titanium alloy. Mater Des. 2016;92:724–30.

    Article  Google Scholar 

  12. Boyer R R, Froes F H S, Chen E Y. High performance metallic materials for cost-sensitive applications. Pennsylvania, America: A Publication of The Minerals, Metals & Materials Society. 2013.

  13. Xun YW, Tan MJ. Applications of superplastic forming and diffusion bonding to hollow engine blades. J Mater Process Technol. 2000;99(1):80–5.

    Article  Google Scholar 

  14. Li ZQ, Guo P. Application progress and development trendency of superplastic forming / diffusion bonding technology. Aviation Manufact Technol. 2010;08:32–5.

    Google Scholar 

  15. Barnes AJ. Superplastic forming 40 years and still growing. J Mater Eng Perform. 2007;16(4):440–54.

    Article  Google Scholar 

  16. Derby B, Wallach ER. Joining methods in space: a theoretical model for diffusion bonding. Acta Astronaut. 1979;7(4–5):685–98.

    ADS  Google Scholar 

  17. Han W, Zhang K, Wang G. Superplastic forming and diffusion bonding for honeycomb structure of Ti–6Al–4V alloy. J Mater Process Technol. 2007;183(2–3):450–4.

    Article  Google Scholar 

  18. Lin J. Selection of material models for predicting necking in superplastic forming. Int J Plast. 2003;19(4):469–81.

    Article  Google Scholar 

  19. Lin J, Cheong BH, Yao X. Universal multi-objective function for optimising superplastic-damage constitutive equations. J Mater Process Technol. 2002;125–126:199–205.

    Article  Google Scholar 

  20. Yang L, Wang B, Liu G, et al. Behavior and modeling of flow softening and ductile damage evolution in hot forming of TA15 alloy sheets. Mater Des. 2015;85:135–48.

    Article  Google Scholar 

  21. Yasmeen T, Shao Z, Zhao L, et al. Constitutive modeling for the simulation of the superplastic forming of TA15 titanium alloy. Int J Mech Sci. 2019;164:105178.

    Article  Google Scholar 

  22. Bai Q, Lin J, Dean TA, et al. Modelling of dominant softening mechanisms for Ti-6Al-4V in steady state hot forming conditions. Mater Sci Eng A. 2013;559:352–8.

    Article  Google Scholar 

  23. Alabort E, Putman D, Reed RC. Superplasticity in Ti–6Al–4V: characterisation, modelling and applications. Acta Mater. 2015;95:428–42.

    Article  ADS  Google Scholar 

  24. Zhang QC, Han YJ, Chen CQ. X-type ultralight lattice structure core (I): concept, material preparation and experiment. Chin Sci. 2009;39(06):1039–46.

    Google Scholar 

  25. Wang J, Evans AG, Dharmasena K, et al. On the performance of truss panels with Kagomé cores. Int J Solids Struct. 2003;40(25):6981–8.

    Article  Google Scholar 

  26. Calamaz M, Coupard D, Girot F. A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti–6Al–4V. Int J Mach Tools Manuf. 2008;48(3):275–88.

    Article  Google Scholar 

  27. Liu Z, Wang X, Jiao X, et al. Prediction of microstructure evolution during hot gas forming of Ti2AlNb-based alloy tubular component with square cross-section. Proc Manufact. 2018;15:1156–63.

    Article  Google Scholar 

  28. Mukherjee AK. An examination of the constitutive equation for elevated temperature plasticity. Mater Sci Eng. 2002;322(1–2):1–22.

    Article  Google Scholar 

  29. Avrami M. Granulation, phase change, and microstructure kinetics of phase change. J Chem Phys. 1941;9(2):177–84.

    Article  ADS  Google Scholar 

  30. Garrett R, Lin J, Dean T. An investigation of the effects of solution heat treatment on mechanical properties for AA 6xxx alloys: experimentation and modelling. Int J Plast. 2005;21(8):1640–57.

    Article  Google Scholar 

  31. Lin J. Fundamentals of materials modelling for metals processing technologies: theories and applications. Imperial College Press. 2015;2015:1–512.

    Google Scholar 

  32. Wu Y, Wang D, Liu Z, et al. A unified internal state variable material model for Ti2AlNb-alloy and its applications in hot gas forming. Int J Mech Sci. 2019;164:105126.

    Article  Google Scholar 

  33. Ma ZY, Mishra RS. Cavitation in superplastic 7075Al alloys prepared via friction stir processing. Acta Mater. 2003;51(12):3551–69.

    Article  ADS  Google Scholar 

  34. Piekło J, Małysza M, Dańko R. Modelling of the material destruction of vertically arranged honeycomb cellular structure. Arch Civil Mech Eng. 2018;18(4):1300–8.

    Article  Google Scholar 

  35. Li J, Wang B, Huang H, et al. Behaviour and constitutive modelling of ductile damage of Ti-6Al-1.5Cr-2.5Mo-0.5Fe-0.3Si alloy under hot tensile deformation. J Alloys Compd. 2019;780:284–92.

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 51805256.

Funding

This research was jointly supported by National Natural Science Foundations of China under Grant No. 51805256.

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Correspondence to Yong Wu.

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Wu, Y., Wu, D., Ma, J. et al. A physically based constitutive model of Ti-6Al-4 V and application in the SPF/DB process for a pyramid lattice sandwich panel. Archiv.Civ.Mech.Eng 21, 106 (2021). https://doi.org/10.1007/s43452-021-00260-0

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  • DOI: https://doi.org/10.1007/s43452-021-00260-0

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