Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws
Abstract
:1. Introduction
2. Materials and Hardening Model
2.1. Materials
2.2. Hardening Models
3. Experiment and Simulation of V-Shaped Bending at Room Temperature
3.1. Experimental Procedure
3.2. Simulation Procedure
3.3. Combined Hardening Law
4. Experiment and Simulation of V-Shaped Bending at Elevated Temperatures
4.1. Experimental Procedure
4.2. Simulation Procedure for V-Bending at Elevated Temperatures
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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C | Si | Mn | P | S | Cr |
---|---|---|---|---|---|
0.19–0.21 | 0.05–0.17 | 0.4–0.6 | 0.04 | 0.05 | ≤0.3 |
Parameters | Levels |
---|---|
Temperature (°C) | 32; 300; 600 |
Bending speed (mm/s) | 1 |
Thickness sheet (mm) | 6 |
Poisson’s ratio | 0.3 |
Young’s modulus (MPa) | 213,000 (32 °C); 184,410 (300 °C); 107,640 (600 °C) |
Temperature (°C) | (MPa) | A (MPa) | B | C (MPa) | γ |
---|---|---|---|---|---|
32 | 348 | 188.86 | 28.3293 | 5350 | 28.3293 |
300 | 199.3 | 171.56 | 3.452 | 592.2251 | 3.452 |
600 | 72.43 | 36.89 | 6.0145 | 221.8749 | 6.0145 |
H (mm) | Bending Angle (°) | Measure Angle θexp (°) | Spring-Back (°) | ||||||
---|---|---|---|---|---|---|---|---|---|
Levels | Average | Levels | Average | ||||||
1 | 2 | 3 | 1 | 2 | 3 | ||||
10 | 136 | 141.5 | 142.5 | 141.5 | 141.833 | 5.5 | 6.5 | 5.5 | 5.833 |
16 | 112 | 117.67 | 117.88 | 119.72 | 118.423 | 5.67 | 5.88 | 7.72 | 6.423 |
22 | 88 | 96 | 95 | 94.5 | 95.167 | 8.0 | 7.0 | 6.5 | 7.167 |
H (mm) | Bending Angle (°) | Measure Angle (°) | Deviation (Δθ)(°) | |||
---|---|---|---|---|---|---|
Experiment () | Simulation () | |||||
Isotropic | Kinematic | Isotropic ( ) | Kinematic ( ) | |||
10 | 136 | 141.83 | 142.50 | 139.05 | 0.667 | −2.783 |
16 | 112 | 118.42 | 119.98 | 117.11 | 1.557 | −1.313 |
22 | 88 | 95.17 | 96.47 | 93.94 | 1.303 | −1.227 |
Bending Angle (°) | Measure Angle (°) | Deviation (Δθ) (°) | |
---|---|---|---|
Experiment () | Simulation () | ||
88 | 95.170 | 95.48 | −0.313 |
112 | 118.423 | 119.11 | 0.686 |
136 | 141.833 | 141.50 | 0.330 |
H (mm) | Bending Angle (°) | Measure Angle (°) | |||||||
---|---|---|---|---|---|---|---|---|---|
300 °C | 600 °C | ||||||||
Level | Avg. | Level | Avg. | ||||||
1 | 2 | 3 | 1 | 2 | 3 | ||||
10 | 136 | 139.1 | 140.15 | 138.9 | 139.38 | 137 | 137.45 | 137.2 | 137.22 |
16 | 112 | 116.2 | 115.5 | 115.2 | 115.63 | 113.15 | 114 | 113.5 | 113.55 |
22 | 88 | 93.5 | 93.0 | 93.0 | 93.167 | 90.5 | 90 | 90 | 90.167 |
T (°C) | (MPa) | (MPa) | (Mpa) | ||
---|---|---|---|---|---|
300 | 199.3 | 53.3422 | 6.9049 | 280.9023 | 2.0133 |
600 | 72.43 | 29.2536 | 6.3814 | 36.5690 | 4.7288 |
Bending Angle (°) | Measure Angle (°) | |||||
---|---|---|---|---|---|---|
300 °C | 600 °C | |||||
Experiment () | Simulation () | Δθ (°) | Experiment () | Simulation () | Δθ (°) | |
88 | 93.167 | 93.86 | 0.693 | 90.167 | 90.52 | 0.353 |
112 | 115.63 | 115.24 | −0.393 | 113.55 | 113.15 | −0.4 |
136 | 139.38 | 138.79 | −0.593 | 137.22 | 136.77 | −0.45 |
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Trieu, Q.-H.; Vuong, G.-H.; Nguyen, D.-T. Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws. Appl. Sci. 2023, 13, 10347. https://doi.org/10.3390/app131810347
Trieu Q-H, Vuong G-H, Nguyen D-T. Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws. Applied Sciences. 2023; 13(18):10347. https://doi.org/10.3390/app131810347
Chicago/Turabian StyleTrieu, Quy-Huy, Gia-Hai Vuong, and Duc-Toan Nguyen. 2023. "Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws" Applied Sciences 13, no. 18: 10347. https://doi.org/10.3390/app131810347
APA StyleTrieu, Q.-H., Vuong, G.-H., & Nguyen, D.-T. (2023). Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws. Applied Sciences, 13(18), 10347. https://doi.org/10.3390/app131810347