# Prediction of Static Recrystallization Nucleation Sites in Tensile Deformed Single Crystal Pure Iron through a Combination of In-Situ EBSD and CP-FEM

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Experimental Setting

#### 2.2. CP-FEM Simulation Setting

## 3. Results and Discussions

#### 3.1. Deformation Characteristics

#### 3.2. Deformation Heterogeneity

#### 3.3. Nucleation Sites—Observation and Prediction

## 4. Conclusions

- Real-world scale CP-FEM calculations on single crystal iron tensile test were compared with experimental observations in four aspects: macroscopic deformation of specimen, load-stroke curve, deformed texture and kernel average misorientation maps. The capability of widely used phenomenological model in reproducing experimentally observed deformation characteristics was evaluated.
- Comparison was made between deformation heterogeneities expressed by KAM derived from EBSD observations and numerical simulations. Around the edges, high deformation heterogeneities were both found in experiments and simulations, while in the central of specimen neck, KAM maps contained more local deformation information than numerically calculated results. Failure in capturing microscale deformation heterogeneity in simulations may be attributed to relatively low grid resolution and incapability of employed constitutive equations in accounting for evolving of discrete dislocation structures inside the material.
- Areas with large distortion concentration in simulation has a qualitative coincidence with approximate nucleation sites in the first stage of recrystallization. This observation justifies the direct application of microstructure simulation methods such as cellular automaton model on energy/distortion distribution derived from CP-FEM for nucleation prediction.
- Experimentally-derived KAM maps have shown similar level of heterogeneity in a large portion of specimen edges. Experimentally observed KAM map is sensitive to local miniature features like zig-zags along edge curvature, surface unevenness, and impurity in specimen.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Boundary condition of CP-FEM simulation model. Upper half of the top pin hole was coupled with a reference point subject to displacement along vertical direction. Lower half of the bottom pin hole was fully constraint through the coupling with another reference point.

**Figure 4.**Specimen profile of specimen 3-1 after deformation (

**a**) measured by SEM; and (

**b**) derived from CP-FEM simulation (units are in mm).

**Figure 5.**Measured and simulated load stroke curves of (

**a**) initial orientation 1; (

**b**) orientation 2; and (

**c**) orientation 3. Crystal lattices before tensile loading were given with black lines highlighting <111> slipping directions. Loading direction was given with red arrow.

**Figure 6.**Comparison between EBSD observed microstructures in the specimen neck region and numerically calculated results after tensile deformation. Only the specimens with larger neck elongation in each initial orientation were presented to save space.

**Figure 7.**Principle of KAM calculation performed on (

**a**) EBSD data; (

**b**) simulation results; P stands for the selected point. Red blocks indicate first order neighbors of the selected point.

**Figure 8.**Kernel average misorientation maps derived from EBSD after tensile deformation of (

**a**) spe. 1-1; (

**b**) spe. 1-2; (

**c**) spe. 2-1; (

**d**) spe. 2-2; (

**e**) spe. 3-1; and (

**f**) spe. 3-2. Dashed lines were used to separate specimens with different initial orientations.

**Figure 9.**Kernel average misorientation maps derived from CP-FEM simulation after tensile deformation of (

**a**) spe. 1-1; (

**b**) spe. 1-2; (

**c**) spe. 2-1; (

**d**) spe. 2-2; (

**e**) spe. 3-1; and (

**f**) spe. 3-2. Dashed lines were used to separate specimens with different initial orientations.

**Figure 10.**Microstructure evolution of specimen 1-2 at annealing time (

**a**) 0 min; (

**b**) 5 min; (

**c**) 15 min; and (

**d**) 60 min. Grain boundaries were highlighted with white lines.

**Figure 11.**Microstructure evolution of specimen 2-2 at annealing time (

**a**) 0 min; (

**b**) 5 min; (

**c**) 30 min; and (

**d**) 60 min. Grain boundaries were highlighted with white lines.

**Figure 12.**Microstructure evolution of specimen 3-1 at annealing time (

**a**) 0 min; (

**b**) 12.83 min; (

**c**) 15 min; and (

**d**) 60 min. Grain boundaries were highlighted with white lines.

**Figure 13.**Microstructure evolution of specimen 3-2 at annealing time (

**a**) 0 min; (

**b**) 10 min; (

**c**) 20 min; and (

**d**) 60 min. Grain boundaries were highlighted with white lines.

**Figure 14.**EBSD measured inverse pole mapping of (

**a**) 1-1 annealed for 60 min; (

**b**) 1-2 annealed for 5 min; (

**c**) 2-1 annealed for 60 min; (

**d**) 2-2 annealed for 30 min; (

**e**) 3-1 annealed for 15 min; and (

**f**) 3-2 annealed for 10 min. Grain boundaries were labeled with solid black lines. These mappings have indicated approximate locations of nucleation sites. Yellow circles pointed out nucleation sites at the first stage of recrystallization. Dashed lines were used to separate specimens with different initial orientations.

**Figure 15.**KAM maps showing locations with top 20% KAM values for specimen (

**a**) 1-1; (

**b**) 1-2; (

**c**) 2-1; (

**d**) 2-2; (

**e**) 3-1; and (

**f**) 3-2 before annealing. Yellow circles pointed out nucleation sites same as those in the previous figure. Dashed lines were used to separate specimens with different initial orientations.

Orientation No. | Specimen No. | Neck Elongation (%) | Initial Crystal Orientation (In Bunge’s Convention) |
---|---|---|---|

Orientation 1 | 1-1 | 15.6 | 146.7, 133.1, 329.2 |

1-2 | 31.1 | ||

Orientation 2 | 2-1 | 17.9 | 272.5, 95.7, 347.8 |

2-2 | 27.3 | ||

Orientation 3 | 3-1 | 27.66 | 60.9, 11.5, 33.8 |

3-2 | 26.86 |

Category | Parameter | Meaning | Value |
---|---|---|---|

Elastic | ${\mathrm{c}}_{11}{,\mathrm{c}}_{12}{,\mathrm{c}}_{44}$ | Elastic coefficient | $229,\text{}134,\text{}115\text{}\left(\mathrm{GPa}\right)$ |

<110> systems | $\mathrm{m}$ | Strain rate sensitivity factor | 0.05 |

${\dot{\mathsf{\gamma}}}_{0}$ | Reference shear rate | 0.01 | |

${\mathrm{h}}_{0}$ | Initial hardening rate | 150.5 (MPa) | |

${\mathsf{\tau}}_{0}$ | Initial critical shear stress | 40.0 (MPa) | |

${\mathsf{\tau}}_{\mathrm{s}}$ | Saturation shear stress | 250.875 (MPa) | |

<112> systems | $\mathrm{m}$ | Strain rate sensitivity factor | 0.05 |

${\dot{\mathsf{\gamma}}}_{0}$ | Reference shear rate | 0.01 | |

${\mathrm{h}}_{0}$ | Initial hardening rate | 67.5 (MPa) | |

${\mathsf{\tau}}_{0}$ | Initial critical shear stress | 58 (MPa) | |

${\mathsf{\tau}}_{\mathrm{s}}$ | Saturation shear stress | 250.0 (MPa) |

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**MDPI and ACS Style**

Luo, Z.; Yoshino, M.; Terano, M.; Yamanaka, A.
Prediction of Static Recrystallization Nucleation Sites in Tensile Deformed Single Crystal Pure Iron through a Combination of In-Situ EBSD and CP-FEM. *Metals* **2018**, *8*, 858.
https://doi.org/10.3390/met8100858

**AMA Style**

Luo Z, Yoshino M, Terano M, Yamanaka A.
Prediction of Static Recrystallization Nucleation Sites in Tensile Deformed Single Crystal Pure Iron through a Combination of In-Situ EBSD and CP-FEM. *Metals*. 2018; 8(10):858.
https://doi.org/10.3390/met8100858

**Chicago/Turabian Style**

Luo, Zichao, Masahiko Yoshino, Motoki Terano, and Akinori Yamanaka.
2018. "Prediction of Static Recrystallization Nucleation Sites in Tensile Deformed Single Crystal Pure Iron through a Combination of In-Situ EBSD and CP-FEM" *Metals* 8, no. 10: 858.
https://doi.org/10.3390/met8100858