Abstract
This study proposes an inverse methodology for determining the strain hardening behaviors at large deformation of titanium alloys using uniaxial tensile and notched tests with finite element analysis. Various hardening laws and data fitting range are considered to characterize the stress-strain relationships of commercially pure titanium (CP-Ti) and Ti6Al4V alloys which can increase the flexibility of identifying the proper models. A new hybrid HHSL hardening model is presented for CP-Ti and its parameters are obtained by iteratively minimizing the difference between the finite element simulation and experimental data. The hardening behavior of Ti6Al4V alloy is predicted by the weighted HSV model. The results show that mechanical response and loading curves from the identified numerical models are consistent with the experimental results of titanium alloys, demonstrating the validity and effectiveness of the proposed inverse approach in practical use.
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Abbreviations
- σ true :
-
True stress
- ε true :
-
True strain
- σ eng :
-
Engineering stress
- ε eng :
-
Engineering strain
- σ :
-
True stress
- ε :
-
Plastic strain
- P 1… P 7 :
-
Hardening model parameters
- Δ1 :
-
Difference between the simulated and experimental stresses
- σ Num Eng :
-
Simulated stress
- σ Exp Eng :
-
Experimental stress
- η :
-
Predefined tolerance of difference between the simulated and experimental stresses
- Δ 2 :
-
Difference between the simulated and experimental forces
- F Num :
-
Simulated force
- F Exp :
-
Experimental force
- ζ :
-
Predefined tolerance of difference between the simulated and experimental forces
- E :
-
Young’s modulus
- σ y :
-
Yield stress
- σ u :
-
Ultimate tensile stress
- ε f :
-
Strain at failure
- A 0 :
-
Initial cross-sectional area
- δl :
-
Elongation in gauge length
- l 0 :
-
Gauge length
- ε max :
-
Strain at the onset of necking
- w :
-
Weighting factor
- σ s :
-
Swift hardening law
- σv :
-
Voce hardening law
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Acknowledgments
This work was supported by the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 21KJB130002) and National Natural Science Foundation of China (Grant No. 11972364).
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Hao Zhang received his Ph.D. from Tianjin University, China, in 2014. Currently, he is a Lecturer in School of Mechanical Engineering, Yangzhou University. His research interests include materials characterization, additive manufacturing, finite element modeling and simulation.
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Zhang, H., Xu, C., Gao, T. et al. Identification of strain hardening behaviors in titanium alloys using tension tests and inverse finite element method. J Mech Sci Technol 37, 3593–3599 (2023). https://doi.org/10.1007/s12206-023-0625-0
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DOI: https://doi.org/10.1007/s12206-023-0625-0