# Simulation of Dynamic and Meta-Dynamic Recrystallization Behavior of Forged Alloy 718 Parts Using a Multi-Class Grain Size Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 2.1. Alloy 718

## 2.2. Double Cone Compression Test

## 2.2.1. Double Cone Geometry

## 2.2.2. Servotest TMTS

## 2.2.3. Initial Grain Size Distribution

## 2.3. Simulation and Multi-Class Grain Size Model

## 2.3.1. DEFORM Simulation

## 2.3.2. Multi-Class Grain Size Model

_{4}is strain rate dependent. As the material builds necklace bands and duplex microstructures, the value for the strain at peak stress

`φ`

_{P}is limited to 0.75, which is relevant for large grain sizes and high strain rates, which led to a satisfying integration of the measured data and literature values.

`φ`

_{C}of the same fraction. By reaching the critical strain

`φ`

_{C}, which is defined in ratio to the strain at peak stress

`φ`

_{P}, the formation of recrystallization nuclei for this fraction begins. The amount of recrystallized fraction by overreaching the critical strain and the resulting grain diameter for every class is simulated with Equations (3) and (4). The kinetics (Equation (3)) with experimentally determined strain (

`φ`

_{0.5}) and strain rates corresponding to the 50% recrystallized volume fraction is represented in this Avrami equation.

## 2.4. EBSD Analysis

^{−2}). Then the specimens were polished with a 3 µm and a 1 µm diamond paste. In order to minimize the effects of previous grinding and polishing processes, the specimens were polished with an alkaline colloidal silica solution (OP-U suspension from Struers) for 20 min and then carefully cleaned with ethanol. The EBSD equipment was a FEI Quanta 250 FEGSEM (Thermo Fisher Scientific Inc., Waltham, MA, USA) equipped with an EDAX AMETEK Hikari XP2 EBSD (AMETEK Materials Analysis Division, Mahwah, NJ, USA) camera, with an acquisition of 15 kV, a spot size of 6 and a 70° tilt angle. The data analysis was performed with the software EDAX-TSL OIM 7.3. (AMETEK Materials Analysis Division, Mahwah, NJ, USA).

## 3. Results

#### 3.1. Recrystallized Fractions

#### 3.1.1. Dynamic Recrystallized Fractions

#### 3.1.2. Meta-Dynamic Recrystallized Fractions

^{−1}and 980 °C. An example for a point of interest at a maximum strain of 0.54 is given in Figure 12b, which shows the time-dependent change of the recrystallizing classes in the multi-class grain size model and the disappearing classes due to MDRX. The beginning of the curves at 3.8 s shows the end of deformation and represents the starting values, which are the results from the DRX calculations.

#### 3.2. Resulting Grain Size Distribution

## 4. Discussion

## 5. Conclusions

- The shift in the DRX is due to delayed water quenching after deformation in all test results. Therefore, the measured recrystallized fraction always includes a certain amount of MDRX. By including the 0.8 s delay in the simulation in case of the tests with 0 s holding time, the fractions are more comparable. Without an in-situ measurement of the microstructure, however, there is no possibility to characterize the condition directly at the end of the forging process.
- For a coarse initial microstructure, the impact of the temperature on MDRX kinetics is higher than the real double cone results have shown. A further adaptation of model parameters and adapted activation energies based on additional double cone experiments shall be done.
- The tendencies that smaller grains recrystallize more easily, i.e., at lower strains is reproduced by the multi-class grain size model. In addition, the increasing amount of nucleation spots with higher strain rates is considered in the model with size-dependent threshold values derived from stress maxima of the flow curves.
- The microstructures of the double cones show normal distributed grain size distributions whereas the multi-class grain size model yields a peak like distribution. This difference can be explained by the advantage of the constant strain rates and temperatures during deformation. As expected, a constant strain rate leads to a homogeneous grain size after recrystallization.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Electron backscatter diffraction (EBSD) inverse pole figure (IPF) maps of microstructures (

**A**,

**B**).

**Figure 6.**Simulation results at four different stages during the compression test. Local total strain during the double cone experiment: 25%—2.00 mm, 50%—4.00 mm, 75%—6.00 mm and 100%—8.00 mm top die displacement; temperature—1020 °C and strain rate—1 s

^{−1}.

**Figure 7.**Flow curves at 1000 °C: (

**a**) two different grain sizes; (

**b**) varying strain rates with Sellars model and experimental data.

**Figure 9.**EBSD grain plot (980 °C, 1 s

^{−1}, strain: 0.54 and 0 s holding time): (

**a**) IPF map, (

**b**) recrystallized grains colored in blue.

**Figure 10.**Recrystallized fraction over time including DRX and MDRX: (

**a**) Comparison of microstructure A with microstructure B: 980 °C, strain rate 1 s

^{−1}, strain 0.54; (

**b**) Comparison of 980 °C and 1020 °C on microstructure A: strain rate 1 s

^{−1}, strain 0.54.

**Figure 11.**Dynamic recrystallization of microstructure A: (

**a**) Recrystallized fractions over strain (980 °C); (

**b**) DRX classes 980 °C, 0.1 s

^{−1}, strain: 0.54.

**Figure 12.**meta-dynamic recrystallization microstructure A: (

**a**) Recrystallized fraction over strain, 0.1 s

^{−1}; (

**b**) MDRX classes 980 °C, 0.1 s

^{−1}, strain: 0.54.

**Figure 13.**Grain size distribution: strain rate 1 s

^{−1}, strain 0.54, 15 s holding time; (

**a**) microstructure A; (

**b**) microstructure B.

Element | Ni [%] | Cr [%] | Fe [%] | Nb [%] | Mo [%] | Ti [%] | Al [%] | Co [%] |
---|---|---|---|---|---|---|---|---|

Min. | 50.00 | 17.00 | - | 4.75 | 2.80 | 0.65 | 0.20 | - |

Max. | 55.00 | 21.00 | Balance | 5.50 | 3.30 | 1.15 | 0.80 | 1.00 |

Parameter | Values |
---|---|

Temperatures (isothermal) | 900 °C, 980 °C, 1000 °C, 1020 °C, 1050 °C |

Strain rates | 0.1 s^{−1}, 1.0 s^{−1}, 10.0 s^{−1}, 50 s^{−1} |

Holding times | 0 s, 5 s, 15 s |

Initial microstructures | 2 different distributions: Microstructure A (coarse) and B (fine) |

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**MDPI and ACS Style**

Gruber, C.; Raninger, P.; Stanojevic, A.; Godor, F.; Rath, M.; Kozeschnik, E.; Stockinger, M.
Simulation of Dynamic and Meta-Dynamic Recrystallization Behavior of Forged Alloy 718 Parts Using a Multi-Class Grain Size Model. *Materials* **2021**, *14*, 111.
https://doi.org/10.3390/ma14010111

**AMA Style**

Gruber C, Raninger P, Stanojevic A, Godor F, Rath M, Kozeschnik E, Stockinger M.
Simulation of Dynamic and Meta-Dynamic Recrystallization Behavior of Forged Alloy 718 Parts Using a Multi-Class Grain Size Model. *Materials*. 2021; 14(1):111.
https://doi.org/10.3390/ma14010111

**Chicago/Turabian Style**

Gruber, Christian, Peter Raninger, Aleksandar Stanojevic, Flora Godor, Markus Rath, Ernst Kozeschnik, and Martin Stockinger.
2021. "Simulation of Dynamic and Meta-Dynamic Recrystallization Behavior of Forged Alloy 718 Parts Using a Multi-Class Grain Size Model" *Materials* 14, no. 1: 111.
https://doi.org/10.3390/ma14010111