# Springback Control in Complex Sheet-Metal Forming Based on Advanced High-Strength Steel

^{*}

## Abstract

**:**

## 1. Introduction

_{p}) had a greater effect on springback than the radius of the corner of the die (R

_{d}). The springback decreased as R

_{p}increased. Lajarin [13] found the blank holder force to be the most important parameter for springback, followed by the die radius and friction conditions. Chen [14], Andersson [15], and Ozturk [16] investigated the blank holder force, punch fillet radius (R

_{p}), and die fillet radius (R

_{d}) using numerical analysis, as well as the model gaps, friction coefficients, model shapes, and other factors affecting springback. Starman [17] proposed a numerical method to optimise the blank shape and tool geometry in a 3D sheet-metal-forming operation, the effects of sheet-metal edge geometry and springback after forming and trimming being considered throughout the optimisation process.

## 2. Experimental Methods

_{0}, r

_{45}, and r

_{90}denote the thick anisotropy coefficients of the specimens along the rolling direction of the plate, at an angle 45° to the rolling direction and perpendicular to the rolling direction in three directions. The stress, σ, is given by:

_{p}denotes the initial strain, ε

_{s}denotes the plastic strain, K denotes the hardening coefficient, and n denotes the hardening index.

_{nom}denote the real and engineering stresses, and ε and ε

_{nom}denote the real and engineering strains.

- Step 1: Establish the strain coordinate system by taking the surface strain ε
_{2}abscissa and surface strain ε_{1}as ordinates. - Step 2: Plot the surface limit strain values (ε
_{2}, ε_{1}), which are measured through experiments in the strain coordinate system. - Step 3: According to the distribution characteristics of the surface limit strains in the coordinate system, connect these points to the appropriate curves. The curve is called the forming limit curve and the coordinate system is called the forming limit diagram.

_{0}points of the sheet and then forming the FLD from the data points of the expansion test. Finally, the FLD can be expressed as follows:

_{1}and d

_{2}denote the parameters to be fitted.

## 3. Results: Forming Quality Evaluation

#### 3.1. The Forming Limit Diagram (FLD)

#### 3.2. Evaluation of the Thinning Rate

#### 3.3. Springback Evaluation

_{z}denotes the maximum value of positive springback, S

_{f}denotes the maximum value of negative springback, and S

_{a}denotes the average of the maximum positive and maximum negative springback values.

## 4. Finite Element Numerical Simulation Design

#### 4.1. Influencing Factors

- (1)
- Friction coefficient

_{N}denotes the pressure.

- (2)
- Model clearance

- (3)
- Blank holder force

- (4)
- Punch fillet radius

#### 4.2. Response Surface Test Design

_{o}is the factor level, F

_{blk}is the blank holder force (KN), R

_{p}is the punch fillet radius (mm), f is the friction coefficient, and X is the model clearance (mm). A total of twenty-seven sets of response surface tests(Table 4) were then designed, with four factors and three levels.

_{a}), as follows:

## 5. Discussion: Stamping Result Optimisation of the Drawing Process

#### 5.1. Multiobjective Optimisation Based on Improved Particle Swarm Algorithm

_{1}and c

_{2}denote acceleration coefficients, r

_{1}and r

_{2}denote random numbers between [0, 1], V

_{i}and X

_{i}denote the velocity and position of the ith particle, and P

_{i}and P

_{g}denote the individual and global extremes.

_{start}denotes the initial inertia weight, ω

_{end}denotes the inertia weight when iterating to the maximum number, and g

_{max}denotes the maximum number of iterations.

_{blk}, R

_{p}, f, X], a maximum number of 100 iterations, and an initial population of 100.

#### 5.2. Springback Compensation

- Step 1: Numerical finite element simulation of the entire process is conducted in DYNAFORM, with corresponding numerical simulations of springback being conducted after each process.
- Step 2: Springback compensation for the drawing process, the shape before springback being the original model and the shape after springback being the shape after springback of the trimming and punching process.
- Step 3: Numerical simulation of the forming finite elements and springback of the entire process, again.
- Step 4: Springback compensation for the flanging and shaping process, the shape before springback being the shape before the springback of the flap-shaping process, and the shape after springback being the result after the springback of the punching and side-punching process.

#### 5.3. Experimental Results Verification

## 6. Conclusions

- (1)
- Uniaxial tension tests at room temperature were conducted on DP590 steel sheeting to obtain the mechanical property parameters and FLD of the material and to establish the evaluation indices of the stamping and forming quality. The FLD can be used to evaluate the forming quality of the part to eliminate ruptures. Consequently, the thinning rate and the average amount of springback met the corresponding production requirements.
- (2)
- A response surface model was established, and the mathematical relationships between the process parameters of the drawing process, the thinning rate, and the average springback were established. The optimal process parameter set was determined using the improved particle-swarm-based multiobjective optimisation algorithm, and the process parameter set with the minimum springback value that guarantees drawing formability was obtained.
- (3)
- Based on the process requirements, a multiprocess springback compensation model that fully considers the springback of each process was developed to ensure that the results met the process requirements. After test stamping, it was evident that the formability was good, no rupture and wrinkling occurred, and the amount of springback was small. These results verified the accuracies of the numerical simulation and optimisation scheme.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Chen, H.; Zhao, L.; Lu, S.; Lin, Z.; Wen, T.; Chen, Z. Progress and Perspective of Ultra-High-Strength Martensitic Steels for Automobile. Metals
**2022**, 12, 2184. [Google Scholar] [CrossRef] - Cao, J.; Banu, M. Opportunities and challenges in metal forming for lightweighting: Review and future work. J. Manuf. Sci. Eng.
**2020**, 142, 110813. [Google Scholar] [CrossRef] - Chen, T.C.; Hsu, C.M.; Wang, C.C. The deep drawing of a flanged square hole in thin stainless steel sheet. Metals
**2021**, 11, 1436. [Google Scholar] [CrossRef] - Zhang, L.C.; Lu, G.; Leong, S.C. V-shaped sheet forming by deformable punches. J. Mater. Process. Technol.
**1997**, 63, 134–139. [Google Scholar] [CrossRef] - Kim, C.; Lee, J.U.; Barlat, F.; Lee, M.G. Frictional behaviors of a mild steel and a TRIP780 steel under a wide range of contact stress and sliding speed. J. Tribol.
**2014**, 136, 021606. [Google Scholar] [CrossRef] - Yang, X.; Choi, C.; Sever, N.K.; Altan, T. Prediction of springback in air-bending of Advanced High Strength steel (DP780) considering Young’s modulus variation and with a piecewise hardening function. Int. J. Mech. Sci.
**2016**, 105, 266–272. [Google Scholar] [CrossRef] - Xue, X.; Liao, J.; Vincze, G.; Pereira, A.B.; Barlat, F. Experimental assessment of nonlinear elastic behaviour of dual-phase steels and application to springback prediction. Int. J. Mech. Sci.
**2016**, 117, 1–15. [Google Scholar] [CrossRef] - Zajkani, A.; Hajbarati, H. Investigation of the variable elastic unloading modulus coupled with nonlinear kinematic hardening in springback measuring of advanced high-strength steel in U-shaped process. J. Manuf. Process.
**2017**, 25, 391–401. [Google Scholar] [CrossRef] - Huang, Y.M.; Chou, I.; Jiang, C.P.; Wu, Y.S.; Lee, S.Y. Finite element analysis of dental implant neck effects on primary stability and osseointegration in a type IV bone mandible. Bio-Med. Mater. Eng.
**2014**, 24, 1407–1502. [Google Scholar] [CrossRef] - Minh, N.Q. Effect of Forming Parameters on Springback of Advanced High Strength Steel DP800. Appl. Mech. Mater.
**2014**, 703, 182–186. [Google Scholar] [CrossRef] - Liu, H.S.; Xing, Z.W.; Bao, J.; Song, B.Y. Investigation of the hot-stamping process for advanced high-strength steel sheet by numerical simulation. J. Mater. Eng. Perform.
**2010**, 19, 325–334. [Google Scholar] [CrossRef] - Seo, D.G.; Chang, S.H.; Lee, S.M. Springback characteristics of steel sheets for warm U-draw bending. Met. Mater. Int.
**2003**, 9, 497–501. [Google Scholar] [CrossRef] - Lajarin, S.F.; Marcondes, P.V.P. Influence of process and tool parameters on springback of high-strength steels. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2015**, 229, 295–305. [Google Scholar] [CrossRef] - Chen, P.; Koc, M. Simulation of springback variation in forming of advanced high strength steels. J. Mater. Process. Technol.
**2007**, 190, 189–198. [Google Scholar] [CrossRef] - Andersson, A. Numerical and experimental evaluation of springback in advanced high strength steel. J. Mater. Eng. Perform.
**2007**, 16, 301–307. [Google Scholar] [CrossRef] - Ozturk, F.; Toros, S.; Kilic, S. Tensile and spring-back behavior of DP600 advanced high strength steel at warm temperatures. J. Iron Steel Res. Int.
**2009**, 16, 41–46. [Google Scholar] [CrossRef] - Starman, B.; Cafuta, G.; Mole, N. A method for simultaneous optimization of blank shape and forming tool geometry in sheet metal forming simulations. Metals
**2021**, 11, 544. [Google Scholar] [CrossRef] - Lingbeek, R.; Huetink, J.; Ohnimus, S.; Petzoldt, M.; Weiher, J. The development of a finite elements based springback compensation tool for sheet metal products. J. Mater. Process. Technol.
**2005**, 169, 115–125. [Google Scholar] [CrossRef] - Li, Y.; Liang, Z.; Zhang, Z.; Zou, T.; Li, D.; Ding, S.; Xiao, H.; Shi, L. An analytical model for rapid prediction and compensation of springback for chain-die forming of an AHSS U-channel. Int. J. Mech. Sci.
**2019**, 159, 195–212. [Google Scholar] [CrossRef] - GB/T 228.1-2010; Metallic Materials—Tensile Testing—Part 1: Method of Test at Room Temperature. State Administration of Supervision, Inspection and Quarantine of the People’s Republic of China. China National Administration Committee: Beijing, China, 2010. (In Chinese)
- GB/T 33965-2017; Metallic Materials—Tensile Testing—Determination of Thickness Reduction Ratio for Rectangular Specimen. State Administration of Supervision, Inspection and Quarantine of the People’s Republic of China. China National Administration Committee: Beijing, China, 2017. (In Chinese)
- GB/T 15825.8-2008; Sheet Metal Formability and Test Methods—Part 8: Guidelines for the Determination of Forming-Limit Diagrams. China Press: Beijing, China, 2008. (In Chinese)
- Xin, J.; Sun, L.; Xiao, X. Numerical simulation and optimization of spring seat drawing process. Hot Work. Technol.
**2011**, 40, 117120. [Google Scholar] [CrossRef] - Yang, L.; Chen, Y.Y.; Wang, Y.L. Study on stamping and forming of metal bipolar plates for fuel cells and thinning rate. Forg. Press. Technol.
**2023**, 48, 56–65. (In Chinese) [Google Scholar] [CrossRef] - Hu, Q. Research and Application of Multi-Objective Particle Swarm Optimization; Beijing University of Chemical Technology: Beijing, China, 2021. (In Chinese) [Google Scholar]

Young’s Modulus E/MPa | Poisson Ratio u | Hardening Coefficient K | Hardening Index n | Anisotropic Parameters | Elongation (%) | Thinning Rate T (%) [21] | ||
---|---|---|---|---|---|---|---|---|

r_{0} | r_{45} | r_{90} | ||||||

201,000 | 0.28 | 950 | 0.179 | 0.71 | 0.96 | 0.71 | 22 | 30 |

n | d_{1} | d_{2} | R^{2} | ||
---|---|---|---|---|---|

Left | Right | Left | Right | ||

0.179 | 4.01184 | −6.9519 | −1.3138 | 0.7920 | 0.960 |

C_{o} | F_{blk} | R_{p} | f | X |
---|---|---|---|---|

−1 | 1200 | 5 | 0.10 | 0.9 |

0 | 1300 | 7 | 0.12 | 0.99 |

1 | 1400 | 9 | 0.14 | 1.08 |

Number | Variable Coded Value | Experiment Result | ||||
---|---|---|---|---|---|---|

F_{blk} | R_{p} | f | X | T | S_{a} | |

1 | −1 | −1 | 0 | 0 | 18.111 | 3.8725 |

2 | 1 | −1 | 0 | 0 | 19.556 | 3.6485 |

3 | −1 | 1 | 0 | 0 | 18.088 | 4.5055 |

4 | 1 | 1 | 0 | 0 | 19.464 | 4.043 |

5 | 0 | 0 | −1 | −1 | 17.873 | 4.4385 |

6 | 0 | 0 | 1 | −1 | 21.356 | 3.038 |

7 | 0 | 0 | −1 | 1 | 17.208 | 5.52 |

8 | 0 | 0 | 1 | 1 | 21.490 | 3.8695 |

9 | −1 | 0 | 0 | −1 | 18.195 | 3.472 |

10 | 1 | 0 | 0 | −1 | 19.223 | 3.4405 |

11 | −1 | 0 | 0 | 1 | 17.903 | 5.2515 |

12 | 1 | 0 | 0 | 1 | 19.536 | 4.233 |

13 | 0 | −1 | −1 | 0 | 17.390 | 4.6235 |

14 | 0 | 1 | −1 | 0 | 17.666 | 5.0785 |

15 | 0 | −1 | 1 | 0 | 21.490 | 3.1805 |

16 | 0 | 1 | 1 | 0 | 21.708 | 3.392 |

17 | −1 | 0 | −1 | 0 | 17.345 | 4.786 |

18 | 1 | 0 | −1 | 0 | 17.686 | 4.6775 |

19 | −1 | 0 | 1 | 0 | 20.218 | 3.4645 |

20 | 1 | 0 | 1 | −1 | 22.413 | 3.1135 |

21 | 0 | −1 | 0 | −1 | 18.643 | 3.397 |

22 | 0 | 1 | 0 | 1 | 18.697 | 3.8175 |

23 | 0 | −1 | 0 | 1 | 18.825 | 4.2495 |

24 | 0 | 1 | 0 | 0 | 18.803 | 4.6255 |

25 | 0 | 0 | 0 | 0 | 18.575 | 3.9795 |

26 | 0 | 0 | 0 | 0 | 18.577 | 3.9642 |

27 | 0 | 0 | 0 | 0 | 18.587 | 3.949 |

_{blk}: blank holder force (KN); R

_{p}: punch fillet radius (mm); f: friction coefficient; X: model clearance (mm); T: thinning rate (%); S

_{a}: average springback.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, Z.; Li, D.; Cao, L.; Cui, H.; Xu, J.
Springback Control in Complex Sheet-Metal Forming Based on Advanced High-Strength Steel. *Coatings* **2023**, *13*, 930.
https://doi.org/10.3390/coatings13050930

**AMA Style**

Lu Z, Li D, Cao L, Cui H, Xu J.
Springback Control in Complex Sheet-Metal Forming Based on Advanced High-Strength Steel. *Coatings*. 2023; 13(5):930.
https://doi.org/10.3390/coatings13050930

**Chicago/Turabian Style**

Lu, Zipeng, Di Li, Linlin Cao, Hongjian Cui, and Jiachuan Xu.
2023. "Springback Control in Complex Sheet-Metal Forming Based on Advanced High-Strength Steel" *Coatings* 13, no. 5: 930.
https://doi.org/10.3390/coatings13050930