Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory
Abstract
:1. Introduction
2. Classical Plasticity Theory
2.1. J2 Deformation Theory
2.2. J2 Flow Theory
3. Experiment and Finite Element Models
3.1. Uniaxial Tensile Test
3.2. Geometrical Model
3.3. Material Model
4. Results and Discussions
4.1. Wrinkling Prediction
4.2. Wrinkle Optimization
5. Conclusions
- The equivalent plastic strain in the redrawing process for manufacturing beverage cans was as small as <0.04.
- J2F underestimated the amplitude and number of wrinkles.
- The amplitude and the number of wrinkles predicted using J2D was shown to be in agreement with the data measured from the sample.
- The stress paths obtained using J2F and J2D were compared to confirm the difference between them and it was confirmed that the stress path obtained using J2D was in the region dominated by compression.
- To optimize the design parameters, the Taguchi method and ANOVA and ANOM analyses were employed along with FE simulations based on J2D.
- The optimal condition for minimizing wrinkle formation was A3B3C1, which means that the S/N ratio of the friction coefficient μ was optimized in level 3 (μ = 0.07), the blank thickness was optimized in level 3 (t = 0.28), and the outer profile angle was optimized in level 1 (α = 34), respectively.
- A simulation with the optimal condition shows the result without wrinkle.
Author Contributions
Funding
Conflicts of Interest
References
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Test Direction | E (GPa) | υ | UTS (MPa) | YS (MPa) | r-Value |
---|---|---|---|---|---|
0° | 69.73 | 0.33 | 310.5 | 281 | 0.41 |
45° | 69.24 | 0.32 | 308.8 | 280 | 0.99 |
90° | 69.41 | 0.33 | 316.8 | 286 | 1.02 |
Factor | Level | ||
---|---|---|---|
1 | 2 | 3 | |
A—Friction coefficient | 0.03 | 0.05 | 0.07 |
B—Can thickness (mm) | 0.25 | 0.265 | 0.28 |
C—Outer profile angle (°) | 34 | 37 | 40 |
Simulation No. | A | B (mm) | C (°) | ∆h (mm) at z = 3.5 mm | S/N Ratio (dB) |
---|---|---|---|---|---|
1 | 0.03 | 0.25 | 34 | 0.01912 | 34.370 |
2 | 0.03 | 0.265 | 37 | 0.07449 | 22.558 |
3 | 0.03 | 0.28 | 40 | 0.01818 | 34.808 |
4 | 0.05 | 0.25 | 37 | 0.15387 | 16.257 |
5 | 0.05 | 0.265 | 40 | 0.02338 | 32.623 |
6 | 0.05 | 0.28 | 34 | 0.00014 | 77.077 |
7 | 0.07 | 0.25 | 40 | 0.08488 | 21.424 |
8 | 0.07 | 0.265 | 34 | 0.00024 | 72.396 |
9 | 0.07 | 0.28 | 37 | 0.00103 | 59.743 |
Factor | by Level (dB) | Degrees of Freedom | SS | Mean Square (%) ** | ||
---|---|---|---|---|---|---|
1 | 2 | 3 | ||||
A | 30.58 | 38.89 | 51.19 * | 2 | 646.2 | 14.82 |
B | 24.02 | 39.43 | 57.21* | 2 | 1656.2 | 37.99 |
C | 61.28* | 32.85 | 26.52 | 2 | 2057.7 | 47.19 |
Total | - | 6 | 4360.1 | 100 |
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Kim, J.J.; Nguyen, P.V.; Kim, Y.S. Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory. Metals 2019, 9, 1168. https://doi.org/10.3390/met9111168
Kim JJ, Nguyen PV, Kim YS. Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory. Metals. 2019; 9(11):1168. https://doi.org/10.3390/met9111168
Chicago/Turabian StyleKim, Jin Jae, Phu Van Nguyen, and Young Suk Kim. 2019. "Prediction of Wrinkling of a Beverage Can Subjected to the Redrawing Process by J2 Deformation Theory" Metals 9, no. 11: 1168. https://doi.org/10.3390/met9111168