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Planar Anisotropy, Tension–Compression Asymmetry, and Deep Drawing Behavior of Commercially Pure Titanium at Room Temperature

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Abstract

The planar anisotropy (PA) and tension–compression asymmetry (TCA) of the CP-Ti were investigated via uniaxial tension and compression tests at room temperature. The formability and the earing behavior of the CP-Ti sheet were studied via deep drawing experiment. The deep drawing simulations using the uniaxial tensile and the compressive curves as the hardening rules were compared with each other and with the experimental results. The CP-Ti sheet showed PA and TCA in yielding and strain hardening. The PA was characterized by the plastic strain ratio r0, r45, and r90 of 1.47, 2.06, and 2.05. The TCA showed PA, which showed tension–compression yield strength ratios of 1.12, 1.08, and 1.04 in 0°, 45°, and 90° in the rolling direction, and tensile and compressive hardening exponent ratios of 0.86, 0.8, and 0.62. The orientation distribution functions (ODFs) analysis demonstrated that the tensile and the compressive deformation textures were different and showed PA. The simulative results, including the simulated forming force and the earing profiles using the uniaxial tensile and compressive curves as the hardening rules, were not in agreement with each other. The results were not in good agreement with the experimental results, implying that the TCA had an important effect on the formability of the sheet. The TCA tended to reduce the thickness of the deep drawing parts, increase the earing ratio, and affect the drawing force.

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References

  1. N.E. Paton and W.A. Backofen, Plastic Deformation of Titanium at Elevated Temperatures, Metall. Trans., 1970, 1(10), p 2839–2847

    Google Scholar 

  2. A. Akhtar and E. Teghtsoonian, Prismatic Slip in α-Titanium Single Crystals, Metall. Mater. Trans. A, 1975, 6(12), p 2201–2208

    Article  Google Scholar 

  3. J.W. Christian and S. Mahajan, Deformation Twinning, Prog. Mater Sci., 1995, 39(1–2), p 1–157. https://doi.org/10.1016/0079-6425(94)00007-7

    Article  Google Scholar 

  4. G. Gilles, W. Hammami, V. Libertiaux, O. Cazacu, J.H. Yoon, T. Kuwabara, A.M. Habraken, and L. Duchêne, Experimental Characterization and Elasto-Plastic Modeling of the Quasi-Static Mechanical Response of TA-6V at Room Temperature, Int. J. Solids Struct., 2011, 48(9), p 1277–1289. https://doi.org/10.1016/j.ijsolstr.2011.01.011

    Article  Google Scholar 

  5. W. Hammami, W. Tirry, F. Coghe, L. Duchêne, L. De Lannay, and A. Habraken, Ti6Al4V Anisolropy and Texture Evolution Predictions Using Multisite and Self Consistent Crystal Plasticity Models, in Ti 2011—Proceedings of the 12th World Conference on Titanium, 2012

  6. A.S. Khan and S. Yu, Deformation Induced Anisotropic Responses of Ti-6Al-4V Alloy. Part I: Experiments, Int. J. Plast, 2012, 38, p 14–26

    Article  Google Scholar 

  7. B. Plunkett, R.A. Lebensohn, O. Cazacu, and F. Barlat, Anisotropic Yield Function of Hexagonal Materials Taking into Account Texture Development and Anisotropic Hardening, Acta Mater., 2006, 54(16), p 4159–4169

    Article  Google Scholar 

  8. S.K. Ghosh, Metal Forming: Mechanics and Metallurgy, J. Mech. Work. Technol, 2nd ed., Prentice Hall, 1985

  9. A. Ghaderi and M.R. Barnett, Sensitivity of Deformation Twinning to Grain Size in Titanium and Magnesium, Acta Mater., 2011, 59(20), p 7824–7839

    Article  Google Scholar 

  10. F. Barlat and K. Lian, Plastic Behavior and Stretchability of Sheet Metals. Part I: A Yield Function for Orthotropic Sheets under Plane Stress Conditions, Int. J. Plast, 1989, 5(1), p 51–66. https://doi.org/10.1016/0749-6419(89)90019-3

    Article  Google Scholar 

  11. A.A. Salem, S.R. Kalidindi, and R.D. Doherty, Strain Hardening of Titanium: Role of Deformation Twinning, Acta Mater., 2003, 51(14), p 4225–4237

    Article  Google Scholar 

  12. C.K. Zhan, Z.Y. Chen, and L. Tang, Anisotropy of Compressive Mechanical Properties of Annealed Pure Titanium Sheet, Zhongnan Daxue Xuebao (Ziran Kexue Ban)/J. Cent. South Univ. (Sci. Technol.), 2012, 43(11), p 4253–4258

    Google Scholar 

  13. T. Hama, H. Nagao, A. Kobuki, H. Fujimoto, and H. Takuda, Work-Hardening and Twinning Behaviors in a Commercially Pure Titanium Sheet under Various Loading Paths, Mater. Sci. Eng. A, 2014, 620, p 390–398

    Article  Google Scholar 

  14. Y. Song, Z. Guan, P. Ma, and J. Song, Theoretical and Experimental Standardization of Strain Hardening Index in Tensile Deformation, Jinshu Xuebao/Acta Metallurgica Sinica, 2006

  15. S. Yi, J. Bohlen, F. Heinemann, and D. Letzig, Mechanical Anisotropy and Deep Drawing Behaviour of AZ31 and ZE10 Magnesium Alloy Sheets, Acta Mater., 2010, 58(2), p 592–605. https://doi.org/10.1016/j.actamat.2009.09.038

    Article  Google Scholar 

  16. T. Ohwue and Y. Kobayashi, Analysis of Earring in Circular-Shell Deep-Drawing of Bcc and Hcp Sheet Metals, Procedia Eng., 2014, 81, p 887–892

    Article  Google Scholar 

  17. W. Tang, S. Huang, D. Li, and Y. Peng, Mechanical Anisotropy and Deep Drawing Behaviors of AZ31 Magnesium Alloy Sheets Produced by Unidirectional and Cross Rolling, J. Mater. Process. Technol., 2015, 215(1), p 320–326

    Article  Google Scholar 

  18. Z. Zs, L. Ry, Y. Mg, C. Cx, G. Jl, and C. Np, Texture Control and the Anisotropy of Mechanical-Properties in Titanium Sheet, J. Mater. Sci., 1997, 32(19), p 5163–5167. https://doi.org/10.1023/A:1018629819791

    Article  Google Scholar 

  19. V. Tuninetti, G. Gilles, O. Milis, T. Pardoen, and A.M. Habraken, Anisotropy and Tension–Compression Asymmetry Modeling of the Room Temperature Plastic Response of Ti-6Al-4V, Int. J. Plast., 2015, 67, p 53–68

    Article  Google Scholar 

  20. Y.B. Chun, S.H. Yu, S.L. Semiatin, and S.K. Hwang, Effect of Deformation Twinning on Microstructure and Texture Evolution during Cold Rolling of CP-Titanium, Mater. Sci. Eng. A, 2005, 398(1–2), p 209–219

    Article  Google Scholar 

  21. N. Bozzolo, N. Dewobroto, T. Grosdidier, and F. Wagner, Recrystallization of Cold Rolled Titanium: The Mechanisms of Texture and Microstructure Evolution, UTBM, Jan 2002, CD-ROM

  22. N. Kotkunde, G. Krishna, S.K. Shenoy, A.K. Gupta, and S.K. Singh, Experimental and Theoretical Investigation of Forming Limit Diagram for Ti-6Al-4V Alloy at Warm Condition, Int. J. Mater. Form., 2017, 10(2), p 255–266

    Article  Google Scholar 

  23. N. Kotkunde, A.D. Deole, A.K. Gupta, and S.K. Singh, Experimental and Numerical Investigation of Anisotropic Yield Criteria for Warm Deep Drawing of Ti-6Al-4V Alloy, Mater. Des., 2014, 63, p 336–344

    Article  Google Scholar 

  24. P.D. Barros, J.L. Alves, M.C. Oliveira, and L.F. Menezes, Modeling of Tension–Compression Asymmetry and Orthotropy on Metallic Materials: Numerical Implementation and Validation, Int. J. Mech. Sci., 2016, 114, p 217–232

    Article  Google Scholar 

  25. M. Vrh, M. Halilovič, B. Starman, B. Štok, D.-S. Comsa, and D. Banabic, Capability of the BBC2008 Yield Criterion in Predicting the Earing Profile in Cup Deep Drawing Simulations, Eur. J. Mech. A Solids, 2014, 45, p 59–74

    Article  Google Scholar 

  26. W. Tang, D. Li, and Y. Peng, Crystal Plasticity Simulation on Earing during Deep Drawing of AZ31 Magnesium Alloy, Zhongguo Youse Jinshu Xuebao Chin. J. Nonferrous Met., 2014, 24(8), p 1933–1940

    Google Scholar 

  27. T. Hama and H. Takuda, Crystal Plasticity Finite-Element Simulation of Work-Hardening Behavior in a Magnesium Alloy Sheet Under Biaxial Tension, Comput. Mater. Sci., 2012, 51(1), p 156–164

    Article  Google Scholar 

  28. M.A. Ablat and A. Qattawi, Numerical Simulation of Sheet Metal Forming: A Review, Int. J. Adv. Manuf. Technol., 2017, 89(1–4), p 1235–1250

    Article  Google Scholar 

  29. C. Liu, On the Asymmetric Yield Surface of Plastically Orthotropic Materials: A Phenomenological Study, Acta Mater., 1997, 45(6), p 2397–2406

    Article  Google Scholar 

  30. O. Cazacu and F. Barlat, A Criterion for Description of Anisotropy and Yield Differential Effects in Pressure-Insensitive Metals, Int. J. Plast., 2004, 20(11 SPEC. ISS.), p 2027–2045

    Article  Google Scholar 

  31. S. Soare, J.W. Yoon, and O. Cazacu, On Using Homogeneous Polynomials to Design Anisotropic Yield Functions with Tension/Compression Symmetry/Assymetry, AIP Conf. Proc., 2007, 908(May), p 607–612

    Article  Google Scholar 

  32. F.B.B. Plunkett and O. Cazacu, Orthotropic Yield Criteria for Description of the Anisotropy in Tension and Compression of Sheet Metals, Int. J. Plast., 2008, 24(5), p 847–866. https://doi.org/10.1016/j.ijplas.2007.07.013

    Article  Google Scholar 

  33. J.W. Yoon, Y. Lou, J. Yoon, and M.V. Glazoff, Asymmetric Yield Function Based on the Stress Invariants for Pressure Sensitive Metals, Int. J. Plast., 2014, 56, p 184–202. https://doi.org/10.1016/j.ijplas.2013.11.008

    Article  Google Scholar 

  34. S.C. Soare and A.A. Benzerga, On the Modeling of Asymmetric Yield Functions, Int. J. Solids Struct., 2016, 80, p 486–500

    Article  Google Scholar 

  35. T. Walde and H. Riedel, Simulation of Earing during Deep Drawing of Magnesium Alloy AZ31, Acta Mater., 2007, 55(3), p 867–874. https://doi.org/10.1016/j.actamat.2006.09.007

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 51505323 and U1302275) and State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology. The authors wish to express their gratitude to the funding.

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Authors and Affiliations

  1. College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    P. Lin, Y. G. Hao, C. Z. Chi & X. L. Cui

  2. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    P. Lin

  3. School of Materials Science and Engineering, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    B. Y. Zhang

  4. School of Materials Science and Engineering, Tongji University, Shanghai, 201804, People’s Republic of China

    J. Shen

  5. Xinzhou City of Quality and Technical Supervision and Inspection and Testing, Xinzhou, 034000, People’s Republic of China

    D. S. Gao

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Correspondence to C. Z. Chi.

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Lin, P., Hao, Y.G., Zhang, B.Y. et al. Planar Anisotropy, Tension–Compression Asymmetry, and Deep Drawing Behavior of Commercially Pure Titanium at Room Temperature. J. of Materi Eng and Perform 28, 1734–1744 (2019). https://doi.org/10.1007/s11665-018-3646-6

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  • DOI: https://doi.org/10.1007/s11665-018-3646-6

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