The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy
Abstract
:1. Introduction
2. Experiments and Results
2.1. Experimental Procedures
2.2. Analysis of Flow Stress Behavior
3. Establishment of the Constitutive Relationship of Annealed TA31
3.1. The Arrhenius-Type Model
3.2. The Modified Johnson–Cook Model
3.3. The Calibration of Material Parameters
4. Comparison of Both Models
5. Conclusions
- The annealed TA31 is a material with negative temperature sensitivity and positive strain rate sensitivity. The dominant deformation mechanism is dynamic recrystallization during low temperatures (˂940 °C), and dynamic recovery during high temperatures (≥940 °C).
- The Arrhenius-type constitutive model considering strain compensation has been established for TA31. The 5th-order polynomial curves are used to describe the relationships between plastic strain and material parameters. The Rco and AARE are 20.09% and 0.9454 based on the parameters obtained by the regression method, respectively. In addition, they are improved to 15.77% and 0.9620 through the global optimization method, respectively.
- The modified Johnson–Cook model incorporating the coupling effect of strain, temperature, and strain rate, as well as the strain-softening phenomenon is used. The new modified JC model has better correlation and smaller errors. Its Rco and AARE are 4.57% and 0.9945 obtained by the calculation of more than 2000 data points, respectively.
- The Arrhenius-type model is not very qualified to accurately represent the flow behavior of annealed TA31, only using one set of parameters over the range of both α and α + β. However, the modified JC model describes the characters of annealed TA31 from dynamic recrystallization to dynamic recovery, leading to the change of the curves’ shape.
- The modified JC model does not only have a simple mathematical expression, but also has the ability to predict the stress of TA31 accurately under a set of model material parameters. It will reduce the cumbersome and complex programming when this model is implemented into the finite element software using the subroutine.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Element | Ti | Al | Nb | Mo | Zr | Fe | C | H | O | N |
---|---|---|---|---|---|---|---|---|---|---|
wt.% | Bal. | 6.08 | 2.94 | 1.02 | 2.02 | 0.038 | 0.005 | 0.001 | 0.071 | 0.003 |
α (MPa−1) | n | lnA (s−1) | Q (J/mol) | |
---|---|---|---|---|
0 | 0.02357 | 3.513363 | 82.93772 | 847,968.6 |
1 | −0.02839 | 0.269352 | −178.989 | −1,786,072 |
2 | 0.149064 | −6.66775 | 681.1676 | 6,839,654 |
3 | −0.28922 | 12.23534 | −1547.92 | −15,672,804 |
4 | 0.263723 | −8.70912 | 1732.279 | 17,655,308 |
5 | −0.10499 | 2.590169 | −760.466 | −7,789,986 |
E0 | E1 | E2 | E3 | E4 | E5 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.05 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | ||||||||||||
K1 | K2 | K3 | K4 | Tm | Tr | ||||||||||||
40 | −0.001 | −0.1 | 0.001 | 1600 | 850 | 0.01 | |||||||||||
F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 | ||||||||||
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
α (MPa−1) | n | LnA (s−1) | Q (J/mol) | |
---|---|---|---|---|
0 | 0.001837 | 6.065099 | 99.73633 | 847,968.9 |
1 | −0.00211 | −2.61215 | −191.982 | −17,86,072 |
2 | 0.023596 | 2.722948 | 690.1866 | 6,839,654 |
3 | −0.06051 | −1.62176 | −1552.48 | −15,672,804 |
4 | 0.07645 | −8.32858 | 1723.548 | 176,55,308 |
5 | −0.03442 | 11.15299 | −753.387 | −7,789,986 |
E0 | E1 | E2 | E3 | E4 | E5 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.3784 | 0.1446 | 0.2165 | 0.1648 | −0.0165 | 0.0040 | ||||||||||||
K1 | K2 | K3 | K4 | Tm | Tr | ||||||||||||
21.8063 | −0.2743 | −1.00 | 0.0017 | 1600 | 850 | 0.01 | |||||||||||
F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 | ||||||||||
−15.1344 | 3.0181 | −1.11674 | 42.8451 | 0.2102 | 0.0128 | 50.00 | −1.1794 |
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Yang, S.; Liang, P.; Gao, F.; Song, D.; Jiang, P.; Zhao, M.; Kong, N. The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy. Materials 2023, 16, 280. https://0-doi-org.brum.beds.ac.uk/10.3390/ma16010280
Yang S, Liang P, Gao F, Song D, Jiang P, Zhao M, Kong N. The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy. Materials. 2023; 16(1):280. https://0-doi-org.brum.beds.ac.uk/10.3390/ma16010280
Chicago/Turabian StyleYang, Shengli, Pei Liang, Fuyang Gao, Dejun Song, Peng Jiang, Min Zhao, and Ning Kong. 2023. "The Comparation of Arrhenius-Type and Modified Johnson–Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy" Materials 16, no. 1: 280. https://0-doi-org.brum.beds.ac.uk/10.3390/ma16010280