Constitutive Model for Equivalent Stress-Plastic Strain Curves Including Full-Range Strain Hardening Behavior of High-Strength Steel at Elevated Temperatures
Abstract
:1. Introduction
2. Summary of Tensile Tests of Q890 High Strength Steel at Elevated Temperatures
3. Procedure for Determining the Equivalent Stress-Plastic Strain Curves of Q890 Steel at Elevated Temperatures
3.1. Determination of Equivalent Stress-Plastic Strain Curves during the Pre-Necking Phase
3.2. Determination of Equivalent Stress-Plastic Strain Curves during the Post-Necking Phase
- Approach I—Iteration procedure for strain-hardening functions
- Approach II—Iteration procedure for equivalent stress (Figure 5)
4. Description of FE Model
5. Constitutive Model for Equivalent Stress-Plastic Strain Curves of Q890 Steel at Different Temperatures
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Temperature (°C) | Elastic Modulus ET (MPa) | Yield Stress fy,T (MPa) | Ultimate Tensile Strength fu,T (MPa) |
---|---|---|---|
20 | 204,976 | 1003 | 1057 |
200 | 204,400 | 893 | 1025 |
300 | 201,032 | 847 | 990 |
400 | 183,367 | 798 | 906 |
450 | 175,592 | 761 | 845 |
500 | 174,246 | 698 | 754 |
550 | 150,692 | 593 | 640 |
600 | 132,509 | 441 | 475 |
700 | 60,189 | 104 | 120 |
800 | 23,209 | 37 | 45 |
T (°C) | Hardening Model | |
---|---|---|
20 | Voce | |
200 | Voce | |
300 | Voce | |
400 | Voce | |
450 | Voce | |
500 | Ludwik |
T (°C) | 800 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
at fracture | 1.006 | 0.719 | 0.985 | 1.08 | 1.35 | 1.95 | 2.29 | 2.22 | 2.92 | 2.3 |
T (°C) | 20 | 200 | 300 | 400 | 450 | 500 | 550 | 600 | 700 | 800 | Mean | Standard Deviation |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1.000 | 0.990 | 0.984 | 1.029 | 1.029 | 0.967 | 1.003 | 0.964 | 1.120 | 0.749 | 0.984 | 0.0889 | |
0.982 | 0.981 | 0.987 | 1.045 | 1.047 | 0.981 | 1.005 | 0.942 | 1.075 | 1.048 | 1.009 | 0.0397 | |
1.000 | 0.998 | 1.002 | 1.002 | 0.999 | 0.997 | 0.998 | 0.999 | 1.020 | 0.058 | 0.907 | 0.2832 | |
1.000 | 1.011 | 1.000 | 0.991 | 1.003 | 0.992 | 1.018 | 0.983 | 1.052 | 0.910 | 0.9960 | 0.0341 |
T (°C) | |||||
---|---|---|---|---|---|
20 | −87.62 | −115.96 | 203.58 | −24.10 | −9.47 |
200 | −14.39 | −192.18 | 206.57 | −136.43 | −42.54 |
300 | −81.13 | −175.81 | 256.94 | −123.61 | −20.24 |
400 | −128.7 | −28.96 | 157.66 | −82.17 | −35.40 |
450 | −89.1 | −109.76 | 198.86 | −137.55 | −8.53 |
500 | −1319.27 | −78.33 | 1397.6 | −0.34 | −104.93 |
T (°C) | C | |||||
---|---|---|---|---|---|---|
550 | −3.9496 | 52.397 | 0.00327 | 9.53 × 10−4 | −2682.4 | −0.1809 |
600 | −0.575 | 37.415 | 0.00394 | 6.82 × 10−4 | −350.94 | −0.764 |
700 | −0.5068 | 16.9 | 0.00341 | 6.33 × 10−4 | −72.98 | −0.9435 |
800 | −0.4473 | 7.606 | 0.00386 | 0.001 | −30.6 | −0.9442 |
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Zeng, X.; Wu, W.; Zou, J.; Elchalakani, M. Constitutive Model for Equivalent Stress-Plastic Strain Curves Including Full-Range Strain Hardening Behavior of High-Strength Steel at Elevated Temperatures. Materials 2022, 15, 8075. https://doi.org/10.3390/ma15228075
Zeng X, Wu W, Zou J, Elchalakani M. Constitutive Model for Equivalent Stress-Plastic Strain Curves Including Full-Range Strain Hardening Behavior of High-Strength Steel at Elevated Temperatures. Materials. 2022; 15(22):8075. https://doi.org/10.3390/ma15228075
Chicago/Turabian StyleZeng, Xiang, Wanbo Wu, Juan Zou, and Mohamed Elchalakani. 2022. "Constitutive Model for Equivalent Stress-Plastic Strain Curves Including Full-Range Strain Hardening Behavior of High-Strength Steel at Elevated Temperatures" Materials 15, no. 22: 8075. https://doi.org/10.3390/ma15228075