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Phenomenological model of hardening and flow for Ti-6Al-4 V titanium alloy sheets under hot forming conditions

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Abstract

Hardening is the core factor to determine deformation uniformity in sheet metal forming. Hot deformation of titanium alloy sheets encounters the coupled effects of strain hardening, strain rate hardening and softening, which makes the determination of forming parameters aiming for an enhanced hardening very difficult in practical processes. This paper presents a new model to quantify the hardening of Ti-6Al-4 V titanium alloy sheets under hot forming conditions based on the underlying correlation between uniform strain and hardening. Firstly, to precisely determine hot deformation characteristics of titanium alloy sheets, hot tensile uniaxial tests using Gleeble systems at various strain rates of 0.01–1 s−1 and temperatures of 973–1123 K were performed systematically. A newly developed volume-based correction method for stress–strain curves of Gleeble thermo-mechanical testing was proposed to eliminate the damaging effect of temperature gradients on strain calculations, which enables the strain hardening, strain rate hardening and softening to be determined precisely. Then, a simple unified formula of hardening components (n, m and s) was proposed to predict the achievable uniform strain at certain conditions efficiently. Using which, occupation of each hardening can be quantified and compared to facilitate the determination of process parameters. Finally, a phenomenological model based on the hardening and softening components was developed to predict the hot flow behaviour. The proposed quantitative model can provide an efficient and useful approach for process designers to design process parameters driven by the objective of enhancing hardening to maximize uniform deformation during hot forming of titanium alloy sheets.

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Abbreviations

\({S}_{NU}^{0}\) (mm2):

Initial cross-section area of non-uniform temperature zone

\({L}_{NU}^{0}\) (mm):

Initial length of non-uniform temperature zone

\({S}_{NU}^{i}\) (mm2):

Instant interface area of between uniform and non-uniform temperature zones

\({L}_{NU}^{i}\) (mm):

Instant length of non-uniform temperature zone

\({S}_{NU}^{I}\) (mm2):

Deformed interface area of between uniform and non-uniform temperature zones

\({L}_{NU}^{I}\) (mm):

Deformed length of non-uniform temperature zones

\(i\) :

Instantaneous time interval

\(I\) :

Total number of time intervals of deformation

\({L}^{i}\) (mm):

Instantaneous length of parallel zone

\({L}_{U}^{i}\) (mm):

Instantaneous gauge length

\({\sigma }_{i}\) (MPa):

Instantaneous true stress

\({P}_{i}\) (N):

Instantaneous deformation force

\({L}_{U}^{0}\) (mm):

Initial gauge length

\({\varepsilon }_{i}\) :

Instantaneous true strain

\(\sigma\) (MPa):

True stress

\(K\) :

Strength coefficient

\(n\) :

Strain hardening exponent

\(\varepsilon\) :

True strain

\({\varepsilon }_{DN}\) :

Strain of diffuse necking

\({\varepsilon }_{LN}\) :

Strain of localized necking

\(m\) :

Strain rate hardening component

\(\dot{\varepsilon }\) (s− 1):

Strain rate

\(s\) :

Softening exponent

\({\varepsilon }_{\text{u}}\) :

Uniform strain

\({\dot{\varepsilon }}^{*}\) (s− 1):

Reference strain rate

\(R\) :

Correlation coefficient

\(AARE\) :

Absolute average relative error

\({E}_{i}\) :

Experimental data

\({P}_{i}\) :

Predicted data

Rest symbols:

Material constants

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Funding

The authors would like to thank the funding support by the National Natural Science Foundation of China (Grant No. 5200052525) and the Fundamental Research Funds for the Central Universities under the Grant Agreement DUT20RC(3)012.

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Authors and Affiliations

  1. School of Material Science and Engineering, Harbin Institute of Technology, Harbin, 15001, China

    Kunning Fu & Shijian Yuan

  2. Shanghai Spaceflight Precision Machinery Institute, Shanghai, 201600, China

    Heli Peng

  3. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Kailun Zheng

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  1. Kunning Fu
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Contributions

Kunning Fu: conceptualization, methodology, writing — original draft preparation, experimental scheme design. Heli Peng: Writing — reviewing and Editing. Kailun Zheng: conceptualization, validation, funding acquisition. Shijian Yuan: supervision.

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Correspondence to Kailun Zheng.

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Fu, K., Peng, H., Zheng, K. et al. Phenomenological model of hardening and flow for Ti-6Al-4 V titanium alloy sheets under hot forming conditions. Int J Adv Manuf Technol 125, 91–103 (2023). https://doi.org/10.1007/s00170-022-10629-x

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