# Research on the Springback Behavior of 316LN Stainless Steel in Micro-Scale Bending Processes

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## Abstract

**:**

## 1. Introduction

## 2. Micro-Scale Four-Point Bending Experiment

#### 2.1. Material Preparation

^{3}kg/m

^{3}was selected to assess size effect and strain gradient size. Three annealing treatments were carried out to eliminate the effect of rolling texture and obtain different grain sizes. To explore the influence of grain size on mechanical behavior in the micro-bending process, the specimen thickness was fixed as 0.1 mm. The heat-treatment conditions and obtained grain sizes are presented in Table 1. The samples were corroded with aqua regia (volume fraction ratio = HCl (37%):HNO

_{3}(68%) = 3:1) for 50 s to obtain the microstructure micrographs shown in Figure 1. The specimens after annealing treatment were isotropic. The plane we used for recording was perpendicular to the thickness direction. The micrographs were observed using a metallurgical microscope (HYZX-2000, Laizhou, China).

#### 2.2. Tensile Tests

^{−3}s

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#### 2.3. Micro-Scale Four-Point Bending Experiments

## 3. A Combined Constitutive Model

#### 3.1. A Combined Constitutive Model

#### 3.2. Constitutive Model Considering Strain Gradient

#### 3.3. The Calculation of Strain, Strain Gradient, Stress and Bending Moment

#### 3.3.1. The Calculation of Strain and Strain Gradient

#### 3.3.2. The Calculation of Stress

#### 3.3.3. The Calculation of Bending Moment

#### 3.3.4. The Calculation of Springback Angle

## 4. Results and Discussion

#### 4.1. Prediction of the Springback Angle

_{E}). In Figure 1a,b, the adopted annealing temperatures are 900 °C and 950 °C, respectively, which do not reach the recrystallization temperature. Therefore, there are few twins in the specimen and the twin effect on the springback angle can be ignored in this research. After conducting the micro-bending tests, the experimental springback angles of the specimens with different grain sizes were compared with the calculation results obtained from the analytical model, which are depicted in Figure 11.

#### 4.2. Factors Contributing to Springback

## 5. Conclusions

- The springback angle of the micro-bending test shows a ‘the smaller, the stronger’ effect, and the springback angle results calculated using the proposed mixed model which considers size effect and strain gradient showed good agreement with the micro-bending experiment data.
- The specially designed four-point bending tooling which allowed the obtainment of a pure bending moment in the bending region made the calculation process easier and ensured that the results were accurate.
- The strain gradient’s effect can be ignored during the micro-bending test that was performed in this study, for the elastic stage of 316LN stainless steel is too obvious, which makes the plastic region small and the strain gradient’s contribution useless, from which it can be inferred that the strain gradient contributes less to materials with obvious elastic stages.
- Quantitative expressions of the factors in the mixed model can be obtained and compared. The geometrical size effect shows a dominant effect compared to the strain gradient, and its contribution to plastic bending angle increases with increasing grain size.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Microstructures of the 316LN stainless steel annealed at (

**a**) 900 °C, (

**b**) 950 °C and (

**c**) 1000 °C.

**Figure 4.**(

**a**) Three-point bending diagram. (

**b**) Four-point bending diagram. (

**c**) Three-point bending shear force diagram. (

**d**) Four-point bending shear force diagram. (

**e**) Three-point bending moment diagram. (

**f**) Four-point bending moment diagram.

**Figure 5.**Experimental tool and corresponding specimens: (

**a**) the structure of the micro-bending tool; (

**b**) a picture of the micro-bending tool; (

**c**) deformed specimens.

**Figure 6.**Schematic identification of the surface and inner grains in a workpiece as a function of overall scale [30].

**Figure 7.**The surface layer model of the sheet samples at the micro-scale [24].

**Figure 10.**Schematic diagram of a sheet (

**a**) after bending and before springback and (

**b**) after springback.

**Figure 12.**Comparison of the contributions of strain gradient and grain and feature size to springback angles in sheet metal samples with different grain sizes.

**Figure 13.**The contribution of strain gradient to springback in sheet metal samples with different grain sizes.

Annealing Conditions | 900 °C, 0.25 h | 950 °C, 0.5 h | 1000 °C, 1 h |
---|---|---|---|

Grain size average (μm) | 18.18 | 29.59 | 40.51 |

Grain size deviation (μm) | 4.54 | 8.86 | 17.33 |

Grain size/sheet thickness (d/t) | 0.18 | 0.30 | 0.41 |

Bar Radius | Pressing Speed | Upper Bar Span (g) | Lower Bar Span (r) | Pressing Distance |
---|---|---|---|---|

1.25 mm | 5 mm/min | 15 mm | 40 mm | 15 mm |

Grain Size (μm) | No.1 (°) | No.2 (°) | No.3 (°) | Average Angle (°) |
---|---|---|---|---|

18 | 46 | 44 | 46 | 45.3 |

30 | 38 | 33 | 40 | 37.0 |

41 | 32 | 33 | 36 | 33.7 |

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**MDPI and ACS Style**

Guo, S.; Tian, C.; Pan, H.; Tang, X.; Han, L.; Wang, J.
Research on the Springback Behavior of 316LN Stainless Steel in Micro-Scale Bending Processes. *Materials* **2022**, *15*, 6373.
https://doi.org/10.3390/ma15186373

**AMA Style**

Guo S, Tian C, Pan H, Tang X, Han L, Wang J.
Research on the Springback Behavior of 316LN Stainless Steel in Micro-Scale Bending Processes. *Materials*. 2022; 15(18):6373.
https://doi.org/10.3390/ma15186373

**Chicago/Turabian Style**

Guo, Shubiao, Chenchen Tian, Haitao Pan, Xuefeng Tang, Lu Han, and Jilai Wang.
2022. "Research on the Springback Behavior of 316LN Stainless Steel in Micro-Scale Bending Processes" *Materials* 15, no. 18: 6373.
https://doi.org/10.3390/ma15186373