Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction
Abstract
:1. Introduction
- (1)
- The new unloading elastic modulus is measured as a straight line between the stress forward and the non-zero residual stress.
- (2)
- Nonlinear regression analysis is used to fit the new model, which is a function of plastic strain.
- (3)
- The implementation of the new model is combined with von Mises yield criteria in finite element software.
- (4)
- The numerical integration of the algorithm stress update is implemented as an implicit integration.
- (5)
- The new model implements two types of nonlinear hardening models, the isotropic model and the combined hardening model, for comparative purposes.
- (6)
- A shell element is used with reduced integration (S4R) due to its efficiency in sheet metal simulation under plane stress conditions.
- (7)
- The extended Chord model was verified by comparing the U-draw bending of DP780 with the pre-strain result, which is available in the Numisheet benchmark 2011.
2. Methods
2.1. New Model Assumption and Statistical Analysis
2.2. Constitutive Models
2.3. Stress Integration
2.3.1. Elastic State Loading and Unloading
2.3.2. Elastic State Unloading and Reloading
2.3.3. Plastic State
3. Application
3.1. Description of Stress-Strain Curve of DP780 Sheet Steel
3.2. Finite Element Simulation to Evaluate New Model
3.3. Draw-Bending Tests to Predict Springback
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
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DP780 | (MPa) | (MPa) | (MPa) | ||||
198,800 | 0.3 | 944 | 454 | ||||
Chord Model | (MPa) | ||||||
460.7 | 39.7 | 152,100 | 96.5 | ||||
QPE Model | (MPa) | (MPa) | (MPa) | ||||
431.62 | 39.7 | 96.9 | 17,135.3 | 95,000 | 254 | 39.7 | |
Extended Model | (MPa) | ||||||
(0.3% ) | 335.7 | 39.7 | 165,407 | 33,083 | 64.59 | 4673.86 | 39.7 |
(0.25% ) | 350.2 | 39.7 | 163,271 | 35,291.7 | 70.5 | 3543.6 | 39.7 |
(0.2% ) | 383.6 | 39.7 | 161,040.9 | 37,577.7 | 77.3 | 3115.9 | 39.7 |
Parameters of Springback | Experiment | Isotropic Model | QPE | Chord Model | 20% | 25% | 30% |
---|---|---|---|---|---|---|---|
115.8 | 103.25 | 119.4 | 105.26 | 120.5 | 116.3 | 111.03 | |
79.2 | 76.5 | 83.3 | 88.33 | 84.2 | 78.67 | 77.1 | |
118.2 | 190.49 | 108 | 82.65 | 105.26 | 117 | 131.89 | |
Errors | |||||||
0% | 10.83% | 3.1% | 9.1% | 4% | 1.43% | 4.1% | |
0% | 3.4% | 5.17% | 11.48% | 6.31% | 2.7% | 3.65% | |
0% | 61.15% | 8.6% | 30% | 10.94% | 2.6% | 11.5% |
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Baara, W.A.B.; Baharudin, B.T.H.T.b.; Anuar, M.K.; Ismail, M.I.S.b. Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction. Metals 2019, 9, 511. https://doi.org/10.3390/met9050511
Baara WAB, Baharudin BTHTb, Anuar MK, Ismail MISb. Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction. Metals. 2019; 9(5):511. https://doi.org/10.3390/met9050511
Chicago/Turabian StyleBaara, Wisam Ali Basher, B. T. Hang Tuah b. Baharudin, Mohd Khairol Anuar, and Mohd Idris Shah b. Ismail. 2019. "Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction" Metals 9, no. 5: 511. https://doi.org/10.3390/met9050511