Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model
Abstract
:1. Introduction
2. Mechanical Model of Profile Stretch-Bending and Springback Analytical Method
2.1. Research Object
2.2. Basic Hypothesis
- (1)
- Plane section assumption: It is assumed that the cross section of profiles before and after stretch-bending loading is planar and perpendicular to the geometrical central axis of the profile.
- (2)
- Uniaxial stress assumption: In the process of stretch- bending, it is assumed that every fiber along axis is in uniaxial tension or uniaxial compression state.
- (3)
- Bilinear material model hypothesis: in the stretch-bending process, it is assumed that stress–strain relationship of the elastic deformation and plastic deformation are both linear.
2.3. Material Model
2.4. Mechanical Model of Stretch-Bending Loading
2.5. Analytical Method of Stretch-Bending Springback
3. Determination of Model Parameters of Proportional Kinematic Hardening Materials
3.1. Geometric Parameters of Profile Cross Section
3.2. Determination of Material Mechanical Property Parameters and Proportional Kinematic Hardening Model Parameters
4. Numerical Simulation of Stretch-Bending
5. Stretch-Bending Experiment
5.1. Experimental Equipment
5.2. Experimental Results and Data Measurement
5.3. Experimental Data Analysis
6. Conclusions
- (1)
- Based on the proportional kinematic hardening model, the analytical expressions for the curvature radius of the strain neutral layer and total moment are obtained after stretch-bending loading. Then, the analytical prediction results of the springback after stretch-bending unloading are obtained based on the plane stretch-bending springback equation.
- (2)
- For the stretch-bending process, when the radius of the bending die does not change, the springback decreases with the increase of tensile force. When the tensile force does not change, the springback increases with the increase of the radius of the bending die.
- (3)
- The experimental results show that the springback analysis based on a proportional kinematic hardening model is more accurate than the results based on a classical kinematic hardening model. Compared with the experimental results of stretch-bending, the accuracy is improved by more than 0.5%.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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B/mm | c/mm | |
---|---|---|
20 | 2 | 1 |
Elastic Modulus E/MPa | Plastic Modulus D/MPa | Yield StressMPa | Elastic Limit Strain |
---|---|---|---|
205,598 | 1127.7 | 178.57 | 0.00086 |
Number | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Tensile stress value/MPa | 190 | 210 | 240 | 270 | 300 |
Reverse yield point/MPa | −172 | −160 | −152 | −139 | −124 |
MPa | MPa | ||
---|---|---|---|
1.2 | 214 | −162 | −0.76 |
1.4 | 250 | −146 | −0.58 |
1.6 | 286 | −130 | −0.45 |
1.8 | 321 | −114 | −0.36 |
2.0 | 357 | −98 | −0.27 |
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Zhai, R.; Zhao, Z.; Yang, J.; Ma, B.; Yu, G. Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model. Symmetry 2021, 13, 2389. https://doi.org/10.3390/sym13122389
Zhai R, Zhao Z, Yang J, Ma B, Yu G. Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model. Symmetry. 2021; 13(12):2389. https://doi.org/10.3390/sym13122389
Chicago/Turabian StyleZhai, Ruixue, Zhuangkun Zhao, Jianhao Yang, Bangbang Ma, and Gaochao Yu. 2021. "Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model" Symmetry 13, no. 12: 2389. https://doi.org/10.3390/sym13122389
APA StyleZhai, R., Zhao, Z., Yang, J., Ma, B., & Yu, G. (2021). Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model. Symmetry, 13(12), 2389. https://doi.org/10.3390/sym13122389