# Study on Asymmetric Rolling Process Applied to Aluminum Alloy Sheets

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Experimental Methods

#### 2.1. Asymmetric Rolling Mill

#### 2.2. Rolling Conditions

#### 2.3. Mechanical Test

#### 2.4. Material

## 3. Brief Description of FLD Code

_{0}) in the form of a narrow band of diminished thickness expressed by the ratio of the initial thickness in the groove to that of the homogeneous region. It is assumed that the material exhibits rigid plastic behavior. The initial yield locus shape is described by the Yld2000-2d plane stress yield criterion of Barlat et al. [22]. Plastic anisotropy is introduced by two linear transformations on the Cauchy stress tensor. The Yld2000-2d plane stress yield function, in terms of the deviatoric stress components, is expressed as:

**s**), which is defined as the deviatoric part of the Cauchy stress:

**C’**and

**C’’**are the material anisotropy coefficients.

- (i)
- The Voce saturation strain-hardening law (Voce):$$\overline{\mathsf{\sigma}}\left(\overline{\mathsf{\epsilon}}\right)=\mathrm{A}-\mathrm{B}\mathrm{exp}(-\mathrm{C}\overline{\mathsf{\epsilon}})$$
- (ii)
- The Swift strain–hardening power law (Swift)$$\overline{\mathsf{\sigma}}\left(\overline{\mathsf{\epsilon}}\right)=\mathrm{K}{\left({\mathsf{\epsilon}}_{0}+\overline{\mathsf{\epsilon}}\right)}^{n}$$

## 4. Results and Discussion

#### 4.1. Mechanical Propeties after Rolling

#### 4.1.1. Yield Stress and Ultimate Tensile Strength

#### 4.1.2. Deformation

#### 4.1.3. Anisotropy

#### 4.2. Recovery Heat Treatment after Rolling

#### 4.3. FLD Prediction

_{0}, σ

_{45}, and σ

_{90}) and three R values (r

_{0}, r

_{45}, and r

_{90}) from uniaxial tension, the biaxial R-value (r

_{b}), and the balanced biaxial yield stress (σ

_{b}), approximated by σ

_{0}, following the observation of Woodthorpe and Pearce [25] for materials exhibiting R values less than 1, since there is no experimental value for it. The exponent “a” of the yield function has a value of 8, which is recommended for materials with a face-centered cubic crystal structure. This parameter controls the sharpness of the yield locus in equibiaxial stretching, which is important in FLD predictions. Table 5 lists the Swift hardening law parameters determined by fitting of experimental true stress–plastic strain curves.

_{45}and σ

_{90}.

_{0}of 0.998, an appropriate value for FCC materials, as suggested by Barlat [26]. An f

_{0}of 0.9998, chosen to increase the predicted values, results in an under evaluation of the left-hand side of the FLD, whereas the right-hand side is substantially overpredicted. The choice of Swift hardening law corroborates a study by Haque and Yoon [25], who found that the Swift law fits better than Voce law for the hardening of the AA6022-T4-T4 sheet. The strain paths are characterized by the stress ratio (α), expressed as σ

_{2}/σ

_{1}, and by the strain ratio (ρ), expressed as dε

_{2}/dε

_{1}, respectively. The acronyms UT, PS, and BS are used for uniaxial tension, plane strain, and biaxial stretching, respectively.

**parameter of Swift law) also leads to a decrease in the FLD curve. After recovery-type annealing, the dislocation density decreases, leading to an increase in the n values and a decrease of ε**

_{0}_{0}compared with the values obtained as a result of ARC conditions. Specifically, the n value of 0.17 after rolling increases to 0.185, which allows for an augmentation of the forming limits compared to those obtained as a result of ARC conditions.

_{0}value. Furthermore, a slight decrease in the forming limits with an increase in the r

_{90}value for low minor strains, as well as an inversion of this effect for larger minor strains, is observed. r

_{45}has no effect on the predicted forming limits. As shown in Figure 14a, following ARC a decrease in the values of r

_{0}and an increase in the values of r

_{90}are observed in all study cases. The decrease in r

_{0}allows for a decrease in the forming limits on the right-hand side of the FLD, whereas an increase in r

_{90}can be associated with a slight increase in the FLD. Because the effect of the r

_{0}value is more pronounced than the r

_{90}effect, a part of the decrease in the FLD after ARC can be attributed to the decrease in the r

_{0}values. The effect of the annealing applied to the material on the anisotropy of the AA6022-T4 sheet is not significant, therefore the increase in the FLD_HT by compared with the FLD_ARC is due to the increase in the material strain hardening after annealing.

## 5. Conclusions

- Symmetric and asymmetric rolling conditions lead to similar results in terms of stress and strain, namely a considerable increase in yield stress (>100%), a moderate increase in ultimate tensile strength (~40%), and a considerable decrease in uniform and total strain (~70–80%);
- The normal anisotropy decreases in the RD direction and increases in the DD and TD directions compared to the Lankford coefficients of material before rolling by approximately 0.2. The planar anisotropy decreases for all routes and shows a dependence on the rolling route, with a minimum for ARC conditions. The maximum reduction, which corresponds to approximately 70%, is reached for ARC_30%_p2. The normal anisotropy shows a very slight increase and is almost insensitive to the rolling routes. However, for the same route, the most considerable increase occurs with ARC_30%_p2, corresponding to 20%. The advantageous evolution of anisotropy can be obtained by the ARC process;
- To increase the formability, annealing in the range of temperatures of 150–175 °C for 30–45 min is recommended;
- The selected constitutive equations, namely the Yld2000-2d yield function and the Swift strain–hardening power law, as well as the FLD code, accurately capture the evolution of the mechanical properties and the formability of an AA6022-T4 sheet through the asymmetric rolling process.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Rolling routes employed in the present work. SR—symmetric rolling; ARC—continuous asymmetric rolling (no rotation of the sheet between two subsequent passes); ARR—reverse asymmetric rolling (rotation around the rolling direction between two subsequent passes).

**Figure 4.**Specimen dimensions: (

**a**) tensile test specimen; (

**b**) plane strain specimen; (

**c**) position of tensile test specimens on the rolled sheet.

**Figure 16.**Experimental and theoretical FLDs of AA6022-T4 sheet using the YLD2000-2d yield function with the Voce law and the Swift law.

Name | Type of Rolling | Reduction per Pass | Pass Number |
---|---|---|---|

AA6022-T4 | Before rolling | - | - |

ARC_10%_p6 | ARC | 10 | 6 |

ARC_15%_p4 | ARC | 15 | 4 |

ARC_30%_p2 | ARC | 30 | 2 |

ARR_10%_p6 | ARR | 10 | 6 |

ARR_15%_p4 | ARR | 15 | 4 |

ARR_30%_p6 | ARR | 30 | 2 |

SR_10%_p6 | SR | 10 | 6 |

SR_15%_p4 | SR | 15 | 4 |

SR_30%_p2 | SR | 30 | 2 |

Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti | Others | Al |
---|---|---|---|---|---|---|---|---|---|

0.8–1.5 | 0.05–0.2 | 0.01–0.11 | 0.02–0.1 | 0.45–0.7 | 0.1 | 0.25 | 0.15 | 0.15 | Balance |

**Table 3.**Mechanical properties of AA6022-T4 (RD, DD, and TD are rolling, diagonal, and transvers direction, respectively).

Yield Stress (MPa) | Ultimate Tensile Stress (MPa) | Uniform Elongation (%) | Total Elongation (%) | R Value | |
---|---|---|---|---|---|

RD | 172.37 | 277.27 | 20.46 | 29.71 | 0.79 |

DD | 166.28 | 273.04 | 23.58 | 33.16 | 0.4 |

TD | 162.18 | 263.95 | 22 | 31.62 | 0.55 |

$\overline{\mathit{R}}$value | ΔR | r_{b} | |||

0.53 | 0.27 | 1.1 |

Material | a | α_{1} | α_{2} | α_{3} | α_{4} | α_{5} | α_{6} | α_{7} | α_{8} |
---|---|---|---|---|---|---|---|---|---|

AA6022-T4 | 8 | 0.97 | 0.99 | 0.87 | 1.05 | 1.01 | 0.99 | 0.93 | 1.19 |

ARC_15%_p4 | 8 | 0.89 | 1.06 | 0.91 | 1.029 | 1.023 | 0.98 | 0.96 | 1.11 |

ARC_30%_p2 | 8 | 0.84 | 1.13 | 0.911 | 1.03 | 1.02 | 0.97 | 0.94 | 1.03 |

ARC_15%_p4_HT | 8 | 0.947 | 0.965 | 0.999 | 1.00 | 1.016 | 0.962 | 0.924 | 0.982 |

ARC_30%_p2_HT | 8 | 0.92 | 1.024 | 0.927 | 1.00 | 1.026 | 1.00 | 0.916 | 0.931 |

Material | K | ε_{0} | n |
---|---|---|---|

AA6022-T4 | 520 | 0.011 | 0.258 |

ARC_15%_p4 | 570 | 0.07 | 0.17 |

ARC_30%_p2 | 590 | 0.07 | 0.17 |

ARC_15%_p4_HT | 605 | 0.05 | 0.185 |

ARC_30%_p2_HT | 615 | 0.05 | 0.185 |

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**MDPI and ACS Style**

Vincze, G.; Pereira, A.B.; Lopes, D.A.F.; Yánez, J.M.V.; Butuc, M.C.
Study on Asymmetric Rolling Process Applied to Aluminum Alloy Sheets. *Machines* **2022**, *10*, 641.
https://doi.org/10.3390/machines10080641

**AMA Style**

Vincze G, Pereira AB, Lopes DAF, Yánez JMV, Butuc MC.
Study on Asymmetric Rolling Process Applied to Aluminum Alloy Sheets. *Machines*. 2022; 10(8):641.
https://doi.org/10.3390/machines10080641

**Chicago/Turabian Style**

Vincze, Gabriela, António B. Pereira, Diogo A. F. Lopes, Jesús M. V. Yánez, and Marilena C. Butuc.
2022. "Study on Asymmetric Rolling Process Applied to Aluminum Alloy Sheets" *Machines* 10, no. 8: 641.
https://doi.org/10.3390/machines10080641