# Influence of Residual Stress around Constituent Particles on Recrystallization and Grain Growth in Al-Mn-Based Alloy during Annealing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

_{3}methanol solution under the condition of about −20 °C or less.

## 3. Results

#### 3.1. Microstructure of Homogenized Specimen

_{6}(MnFe) and α-Al(Mn, Fe)Si, the backscattered electron image is presented in Figure 2b. A large quantity of primary particles with rod-like, plate-like, and network eutectic shape are distributed in the grain boundaries and inside the inter-dendritic area (Figure 2a,b), where primary particles consist of α-Al(Mn, Fe)Si phases and less amount of Al

_{6}(Mn, Fe) phases with an average size of 2.5 μm. The Al

_{6}(Mn, Fe) phase was transformed to a large number of α-Al(Mn, Fe)Si phase, which can be clearly identified in the backscattered electron image (BEI) of the as-cast specimen and the homogenized specimens (Figure 2b), where the α-Al(Mn, Fe)Si phase exhibits brighter contrast than the Al

_{6}(Mn, Fe) phase. A large number of fine secondary particles were homogeneously formed in the Al matrix due to the effect of the homogenization treatment. It is noted that dislocation networks were frequently observed around the smaller precipitate with a diameter of 459 nm at the interior of the grain, which is enclosed by the dislocation walls (Figure 2c). The quantitative values of grain size, primary particle size, and electric conductivity are listed in Table 3. Since the electric conductivity of as-homo specimen was significantly increased as compared to that of as-cast specimen, the amount of concurrent precipitation during the recovery and recrystallization stages is potentially reduced by homogenization treatment.

#### 3.2. Change in Microstructure with Increase of Strain

_{t}, the nominal strain is ε

_{n}, the reduced thickness of the cold rolled sheet is t

_{1}, and the initial thickness of the sheet is ${t}_{0}$.

_{t}≤ 0.69), while the volume fraction of the grains with HAGB is increased in the AM9 specimen (Figure 3e). This implies that high-angle boundaries are newly developed by further plastic deformation, which leads to grain fragmentation due to the higher strain [27]. It is clearly seen from Figure 3b,d,f, which are the higher magnification images taken from ND; dislocation microstructure is composed of sub-grain boundaries (Figure 3b) and dislocation cells (Figure 3b,d). On the other hand, the strain contrast of AM9 is difficult to identify the boundaries clearly, which is due to the dense dislocations introduced by heavily plastic deformation (Figure 3f).

#### 3.3. Deformation Zone around the α-Al(Mn, Fe)Si Precipitate with Increase of Strain

#### 3.4. Evolution of Dislocation Density with Increasing Strain

_{t}= 0.22) is not significantly different from that of as-homo (ε

_{t}= 0.0), but the diffraction angle is shifted slightly toward the lower angle. This shift of diffraction angle implies an increase of d-spacing in ND direction as a result of residual strain. The profile of AM5 (ε

_{t}= 0.69) shows the broadening of diffraction peak at the similar peak position of AM2 (ε

_{t}= 0.22). As the amount of reduction is increased, further broadening occurs, but the diffraction peak position is not significantly changed in AM9 (ε

_{t}= 2.30). Accounting for the peak broadening with an increase of the amount of plastic deformation, inhomogeneous strain distribution and a small crystallite of a cold-rolled specimen are suggested.

_{L}, on the value of the full width at half maximum (FWHM) obtained from each peak can be mentioned as follows, [30].

_{t}= 1.5. This consistency might be due to the fact that the crystallite observed by TEM is mainly composed of the fine equi-axed grains (Figure 3). It should be mentioned that the thickness of HAGBs by TEM analysis is consistent with the theoretical prediction by Equation (1).

^{14}m

^{−2}for AM2, 2.68 × 10

^{14}m

^{−2}for AM5 and 3.87 × 10

^{14}m

^{−2}for AM9. Accounting for the facts of the similar slopes for lattice strains in Figure 9a and the linear relationship between the crystallite size and the lattice strain in Equation (4), the change in dislocation density at the larger plastic strain is attributed to the change in crystallite size D as shown in Figure 9a and Figure 10.

#### 3.5. Recrystallization Behavior in Cold Rolled Specimen with Different Reduction Ratio

^{14}m

^{−2}, 0.87 × 10

^{14}m

^{−2}and 0.78 × 10

^{14}m

^{−2}, respectively.

## 4. Discussions

#### 4.1. Evolution of Dislocation Density

#### 4.2. Driving Force for Recrystallization

_{b}under cold rolling conditions are important when discussing the mobility of grain boundaries during annealing. The energy of simple tilt boundary is given by Read-Shockley [38].

_{max}is high angle boundary (commonly considered 15 degrees) and γ

_{max}is the value of boundary energy when the boundary is at a high angle. γ

_{max}is considered to be 0.324 J/m

^{2}in the aluminum [39].

_{d}, can be estimated from the dislocation density in view of self-energy of dislocations.

_{2}is the pre-factor for dislocation energy (0.5 is often used for self-energy of dislocation by line tension approximation). Substituting dislocation densities calculated in the present study, 1.66 × 10

^{14}m

^{−2}for AM2, 2.68 × 10

^{14}m

^{−2}for AM5 and 3.87 × 10

^{14}m

^{−2}for AM9, and material constants, G = 2.6 × 10

^{10}N/m

^{2}, b = 0.286 nm, stored energy for AM2, AM5, and AM9 amounts to 3.1 × 10

^{5}, 4.9 × 10

^{5}and 7.1 × 10

^{5}J/m

^{3}, respectively. Accounting for the equilibrium of thermodynamic pressure, critical radius of recrystallized grain can be predicted by the following formula,

_{b}is the grain boundary energy for 0.324 J/m

^{2}in the aluminum, and E

_{d}is the stored energy (thermodynamic pressure).

#### 4.3. Thermodynamic Pressure for Boundary Migration

^{5}J/m

^{3}(the as-rolled), 2.8 × 10

^{5}J/m

^{3}(annealed at 350 °C for 2 min), and 2.7 × 10

^{5}J/m

^{3}(annealed at 400 °C for 2 s). Hence, the energy consumption at 350 °C and 400 °C during the recovery stage amounted to 8.1% and 11.1%, respectively. These results are consistent with the consumed energy as reported in [41], where 10% of the stored energy is consumed in the recovery process.

_{net}that acted on the boundary of recrystallized grain is given as,

_{d}, P

_{p}and P

_{c}, respectively. α is a constant of the order of 0.5, G is the shear modulus, f

_{v}is the volume fraction of second-phase particle, γ

_{b}is the boundary energy, and d is the diameter of particle. Recalling the results of Section 3.2 and Section 3.4, it can be seen that the net driving pressure associated with dislocation density and curvature of boundary affecting the nucleation and growth rate of recrystallized grains in AM9 is greater than AM2 and AM5 with lower plastic deformation.

#### 4.4. Residual Stress of α-Al(Mn, Fe)Si Particle

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic diagram of DC casting direction and dimensions, (

**b**) positions of a sample taken from the ingots for a test, and (

**c**) dimensions of cold-rolled sheets.

**Figure 2.**The typical microstructure of homogenized AA3003 aluminum alloy observed by (

**a**) OM, (

**b**) SEM-BEI, (

**c**) TEM.

**Figure 3.**Representative TEM bright images of cold-rolled AA3003 aluminum alloy with different amounts of reduction. (

**a**,

**b**) 20%, (

**c**,

**d**) 50%, and (

**e**,

**f**) 90%.

**Figure 4.**EBSD map around the α-Al(Mn, Fe)Si precipitate in the longitudinal section of the cold-rolled AA3003 aluminum alloy with different amounts of reduction, (

**a**) 20%, (

**b**) 50%, and (

**c**) 90%. The inverse pole figures (IPF) indicate the color key of the crystal direction parallel to the normal direction (ND).

**Figure 5.**(

**a**) Kernel average misorientation map of AM5 indicated in Figure 4b (region 1) with the arrow marking (

**b**) misorientation profile.

**Figure 6.**Misorientation angle profiles of (

**a**,

**d**) AM2, (

**b**,

**e**) AM5, and (

**c**,

**f**) AM9 across the rotated zone formed around α-Al(Mn, Fe)Si precipitate. The point-to-point line (black) indicates the profile of the orientation changes between adjacent point. The point-to-origin line (red) represents the profile of the orientation changes between all points and origin point.

**Figure 7.**Changes in the number fraction of the LAGBs and HAGBs, and Vickers hardness with increase of the amount of reduction in the AA3003 aluminum.

**Figure 8.**(111) diffracted peak at different amounts of reduction for the DC cast AA3003 aluminum alloy with homogenization.

**Figure 9.**(

**a**) Williamson-Hall plots and (

**b**) Crystallite size of the cold-rolled AA3003 aluminum alloy measured by XRD and TEM.

**Figure 10.**Evolution of the HAGB thickness, crystallite size, and dislocation density with increasing the logarithmic strain in the AA3003 aluminum alloy.

**Figure 11.**Evolution of the recrystallization microstructure for the AM2, AM5, and AM9 at 350 °C for different holding times.

**Figure 12.**Change in the dislocation density as a function of annealing time at (

**a**) 350 °C and (

**b**) 400 °C in AM2, AM5, and AM9.

**Figure 15.**Schematic diagram for formation and coalescence of sub-grains during annealing. (

**a**) cold-rolled structure with low plastic deformation, (

**b**) formation of subgrain during recovery and (

**c**) coalescence of the subgrain by subsequent annealing.

**Figure 16.**Evolution of the dislocation density and crystallite size as a function of annealing time at 350 °C and 400 °C in (

**a**) AM2, (

**b**) AM5, and (

**c**) AM9.

**Figure 17.**Grain orientation spread (GOS) map overlaid with IPF map in AM9 annealed at 300 °C for 30 s shows growth of recrystallized grain (

**a**) in deformation zone around a coarse particle and (

**b**) in dispersoid zone.

**Figure 18.**Deformed shape and residual stress around the spherical inhomogeneity (α-Al(Mn, Fe)Si precipitate) under cold-rolling condition ($\Delta {\epsilon}_{33}^{\mathrm{p}}$ = $-\Delta {\epsilon}_{11}^{\mathrm{p}}$ = 0.5, and $\Delta {\epsilon}_{22}^{\mathrm{p}}$ 0) are represented in (

**a**) ${\sigma}_{11}$ and (

**b**) ${\sigma}_{33}$. The displacement and residual stress outside the inhomogeneity are deduced from Equations (17) and (9), respectively.

**Figure 19.**Misorientation angles profile across the rotated zone formed around the α-Al(Mn, Fe)Si precipitate measured by the prediction of displacement gradient and EBSD analysis.

Alloy | Mn | Cu | Fe | Si | Ti | Al |
---|---|---|---|---|---|---|

AA3003 | 1.15 | 0.16 | 0.52 | 0.28 | 0.01 | bal. |

**Table 2.**Young’s modulus and Poisson ratio for aluminum matrix and α-Al(Mn, Fe)Si precipitate. The subscripts m and p indicate matrix phase and precipitate.

**Table 3.**Change of grain size, primary particle size, and electrical conductivity in the DC cast AA3003 aluminum alloy by homogenization.

Condition | Average Grain Size (μm) | Average Primary Particle Size (μm) | Electric Conductivity (%IACS) |
---|---|---|---|

As-cast | 140 | 2.8 | 30 |

As-homo | 160 | 4.1 | 43.5 |

**Table 4.**Comparison of the residual stress inside the α-Al(Mn, Fe)Si precipitate with sphere computed by Equation (9) under cold-rolling condition (${\epsilon}_{11}^{0}$ = $-{\epsilon}_{33}^{0}$ = 0.2, 0.5 and 0.9, and ${\epsilon}_{22}^{0}$ = 0). Von Mises Equivalent stress, ${\sigma}_{\mathrm{eqv}}$, is computed by Equation (16).

${\mathit{\epsilon}}_{\mathbf{ij}}^{0}$ | ${\mathit{\sigma}}_{\mathbf{ij}}/\mathbf{GPa}$ | |||
---|---|---|---|---|

${\mathit{\sigma}}_{11}$ | ${\mathit{\sigma}}_{22}$ | ${\mathit{\sigma}}_{33}$ | ${\mathit{\sigma}}_{\mathbf{eqv}}$ | |

0.2 | 8.25 | <10^{−17} | −8.25 | 14.29 |

0.5 | 20.62 | <10^{−17} | −20.62 | 35.72 |

0.9 | 37.12 | <10^{−17} | −37.12 | 64.29 |

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Park, S.-J.; Muraishi, S.
Influence of Residual Stress around Constituent Particles on Recrystallization and Grain Growth in Al-Mn-Based Alloy during Annealing. *Materials* **2021**, *14*, 1701.
https://doi.org/10.3390/ma14071701

**AMA Style**

Park S-J, Muraishi S.
Influence of Residual Stress around Constituent Particles on Recrystallization and Grain Growth in Al-Mn-Based Alloy during Annealing. *Materials*. 2021; 14(7):1701.
https://doi.org/10.3390/ma14071701

**Chicago/Turabian Style**

Park, Sung-Jin, and Shinji Muraishi.
2021. "Influence of Residual Stress around Constituent Particles on Recrystallization and Grain Growth in Al-Mn-Based Alloy during Annealing" *Materials* 14, no. 7: 1701.
https://doi.org/10.3390/ma14071701