Manufacturing Technology 2026, 26(2):239-248 | DOI: 10.21062/mft.2026.021

Finite Element Secondary Development of Constitutive Model for Titanium Alloy Vibration-Assisted Cold Upsetting Forming

Xu Yani ORCID..., Wang Ying ORCID..., Wei Chuhan ORCID..., Lin Kai ORCID..., Shu Xuedao ORCID...
School of Mechanical Engineering and Intelligent Manufacturing, Ningbo University, No. 818 Fenghua Road, Jiangbei District, Ningbo, Zhejiang Province, China

To achieve precise finite element simulation of the vibration-assisted cold heading process of titanium alloys, this study focuses on Ti-45Nb titanium alloy as the research object. A constitutive model for vibration-assisted cold heading is established, incorporating both viscoelastic and viscoplastic deformation. The model is transformed into a programmable incremental form, and the control equations for elastic-viscoplastic deformation are derived. Secondary development is conducted using the VUMAT interface of ABAQUS, and the model is applied in simulation. Multi-condition simulations of Ti-45Nb titanium alloy cold heading are performed, and the results are compared with experimental data. The average relative error is found to be within 5%, verifying the accuracy of the finite element numerical simulation based on the secondary development. The developed constitutive model is used to simulate the cold heading process of Ti-45Nb titanium alloy internal wire joint components. The significant effects of vibration assistance in reducing maximum stress, optimizing stress distribution, and improving material flow are intuitively observed. This study provides technical support for the application of vibration-assisted cold heading technology in the forming of difficult-to-deform materials.

Keywords: Cold upsetting forming, Vibration assistance, VUMAT subroutine, Constitutive model, Finite element simulation
Grants and funding:

The Project is supported by Ningbo "Science and technology innovation Yongjiang 2035" key research and development program（2024Z169)

Received: July 1, 2025; Revised: April 10, 2026; Accepted: April 14, 2026; Prepublished online: April 20, 2026; Published: April 23, 2026  Show citation

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Yani X, Ying W, Chuhan W, Kai L, Xuedao S. Finite Element Secondary Development of Constitutive Model for Titanium Alloy Vibration-Assisted Cold Upsetting Forming. Manufacturing Technology. 2026;26(2):239-248. doi: 10.21062/mft.2026.021.
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    References

    1. LU, W. H. (2023). Research and improvement of multi-station cold forging process for automotive flange connecting parts based on numerical simulation. Forging & Stamping Technology, Vol. 48, No. 2, pp. 29-35+110. DOI: 10.13330/j.issn.1000-3940.2023.02.004. Go to original source...
    2. CHENG, M. W., LIU, F. L., LI, W. Q., et al. (2020). Research on the microstructure evolution law of multi-station heading forming of stainless steel high lock nuts. Hot Working Technology, Vol. 49, No. 5, pp. 103-107. DOI: 10.14158/j.cnki.1001-3814.20183526. Go to original source...
    3. YU, F. Q., FANG, Z. L. (2023). Research on ultrasonic vibration-assisted milling process for titanium alloy thin-walled parts. Mechanical and Electrical Engineering, Vol. 40, No. 1, pp. 129-135.
    4. LI, Y. B., LIU, T. D. (2022). Research on the microstructure and properties of cast TC4 titanium alloy. Hot Working Technology, Vol. 51, No. 21, pp. 65-68. DOI: 10.14158/j.cnki.1001-3814.20211439 Go to original source...
    5. QI, Z. C., XIAO, Y. X., WANG, X. X., et al. (2021). Analysis of the forming performance of Ti45Nb rivets under pulse current-assisted pressing. China Mechanical Engineering, Vol. 32, No. 23, pp. 2832-2839, 2849.
    6. TENG, X. Y. (2021). Simulation research on the flexible coupling model of the transmission mechanism of high-speed cold heading machine. Jinan University.
    7. YANG, L. J., CHEN, X., SUN, B. S. (2023). Simulation analysis of the forming law of TC4 titanium alloy tube under vibration-assisted forming. Hot Working Technology, Vol. 52, No. 5, pp. 102-107. DOI: 10.14158/j.cnki.1001-3814.20210219 Go to original source...
    8. HU, J., SHIMIZU, T., YOSHINO, T., et al. (2018). Ultrasonic dynamic impact effect on deformation of aluminum during micro-compression tests. Journal of Materials Processing Technology, Vol. 258, pp. 144-154. DOI: 10.1016/j.jmatprotec.2018.03.021 Go to original source...
    9. ZHANG, H. D., DENG, L., WANG, X. Y., et al. (2020). Research progress on the mechanism and application of vibration-assisted plastic forming. Aeronautical Manufacturing Technology, Vol. 63, No. 16, pp. 22-31. DOI: 10.16080/j.issn1671-833x.2020.16.022 Go to original source...
    10. GUO, L. G., WANG, F. Q., LIANG, L., et al. (2017). New ideas and research progress on intelligent simulation optimization of high-performance ring rolling forming. Precision Forming Engineering, Vol. 9, No. 4, pp. 1-11. DOI: 10.3969/j.issn.1674-6457.2017.04.001 Go to original source...
    11. WANG, Z. J., WANG, Z. W. (2024). Simulation research on metal tensile testing based on J-C constitutive model. Xinjiang Steel, No. 2, pp. 31-33.
    12. WANG, Z., YIN, H. (2025). Titanium Alloy Turning Machining Model and Quality Analysis Based on Finite Element Analysis. Manufacturing Technology, Vol. 25, No. 3, pp. 413-423. DOI: 10.21062/mft.2025.036. Go to original source...
    13. KIRCHNER, H. O. K., KROMP, W., PRINZ, F. B., et al. (1985). Plastic deformation under simultaneous cyclic and unidirectional loading at low and ultrasonic frequencies. Materials Science and Engineering, Vol. 68, No. 2, pp. 197-206. DOI：10.1016/0025-5416(85)90409-4 Go to original source...
    14. CAI, G. P., LIU, Z., ZHAN, H. (2008). Volume effect analysis of metal deformation with low-frequency pulse vibration. Forging & Stamping Technology, No. 5, pp. 155-159.
    15. WANG, J. P., ZHAO, Z., ZHUANG, X. C., et al. (2015). Study on constitutive model of ultrasonic vibration-assisted forming. Journal of Plasticity Engineering, Vol. 22, No. 6, pp. 1-6. DOI: 10.3969/j.issn.1007-2012.2015.06.001 Go to original source...
    16. SIDDIQ, A., SAYED, T. E. (2011). Acoustic softening in metals during ultrasonic assisted deformation via CP-FEM. Materials Letters, Vol. 65, No. 2, pp. 356-359.DOI: 10.1016/j.matlet.2010.10.029 Go to original source...
    17. MELLER, A., LEGUTKO, S., MRÓZ, A., et al. (2024). Enhancing Durability of Multi-Cavity Forging Tools through Process Automation. Manufacturing Technology, Vol. 24, No. 6, pp. 929-939. DOI: 10.21062/mft.2024.105. Go to original source...
    18. LIU, Z. J. (2024). Research on titanium alloy milling simulation platform and cutting characteristics based on Abaqus. Shenyang Ligong University. DOI: 10.27323/d.cnki.gsgyc.2024.000672. Go to original source...
    19. Zeng X. G., Chen H. Q., Chen J., (2016) Viscoelastic Mechanics. Chengdu: Sichuan University Press.
    20. Yao Z., Kim G. Y., Wang Z., et al. (2012) Acoustic softening and residual hardening in aluminum: modelling and experiments[J]. International Journal of Plasticity, 2012, 39: 75-87. DOI: 10.1016/j.ijplas.2012.06.003 Go to original source...
    21. NAGODE M., KLEMENC J., OMAN S., et al. (2024) Elasto-viscoplastic material modelling using the multiaxial Prandtl operator approach. International Journal of Mechanical Sciences, Vol. 267, pp. 108953. DOI: 10.1016/j.ijmecsci.2023.108953 Go to original source...
    22. LIN, J., PRUNCU, C., ZHU, L., et al. (2022). Deformation behavior and microstructure in the low-frequency vibration upsetting of titanium alloy. Journal of Materials Processing Technology, Vol. 299, p. 117360. DOI: 10.1016/j.jmatprotec.2021.117360. Go to original source...
    23. SHI, Y. P., ZHOU, Y. R. (2006). ABAQUS Finite Element Analysis Example Explanation. Beijing: Mechanical Industry Press.
    24. ZHENG, B. (2024). Analysis of Static and Dynamic Characteristics and Lightweight Design of Titanium Alloy Frame. Manufacturing Technology, Vol. 24, No. 3, pp. 507-519. DOI: 10.21062/mft.2024.053. Go to original source...

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