# Molecular Dynamics Simulation of High-Temperature Creep Behavior of Nickel Polycrystalline Nanopillars

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Method and Process

#### 2.1. Main Variables

^{3}. The number of grains varied from 10 to 30 in five models, see Figure 1. Through approximating grains as spheres, the corresponding averaged diameter $\overline{d}$ can be calculated by $\overline{d}=\sqrt[3]{3V/\left(4\pi N\right)}$, in which V and N are the volume of the model and the number of grains in the model, respectively. Table 2 shows the grain size of each model.

#### 2.2. Main Process of Simulations

## 3. Results and Analysis of Simulations

#### 3.1. Nano-Tensile Test Simulations

#### 3.2. Nano-Creep Simulations

#### 3.3. Thermally Activated Mechanisms

## 4. Discussion on Creep Mechanisms

#### 4.1. Deformation Diagram for NC Ni

#### 4.2. Creep through Dislocations

#### 4.3. Creep Through Grain Boundary Sliding

#### 4.4. Grain Size Effect

## 5. Summary

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**–

**e**) Five models with different numbers of grains, named M1 to M5 for model 1 to model 5. These pictures are visualized by a polyhedral template matching (PTM) method [33] in OVITO (green: FCC; red: others as grain boundary). (

**a**) M1: 30 grains, (

**b**) M2: 25 grains, (

**c**) M3: 20 grains, (

**d**) M4: 15 grains, (

**e**) M5: 10 grains.

**Figure 2.**The results of nano-tensile simulations. (

**a**) Stress–strain curves at the corresponding temperatures for M1. (

**b**) The temperature dependence of the tensile strength ${R}_{\mathrm{m}}$. (

**c**) The influence of the grain size on the tensile strength ${R}_{\mathrm{m}}$.

**Figure 3.**(

**a**) Creep curves of model M1 for different stresses at 1000 K. (

**b**) The log–log scaling plot of creep rates $\dot{\epsilon}$ over $\sigma $ at different temperatures. The data are split up into a low $\sigma $ region and a high $\sigma $ region and were fitted with different exponents n. (

**c**) The relationship between the stress exponent n and temperature.

**Figure 4.**(

**a**) The plot of $ln\dot{\epsilon}$ versus $1/\left({k}_{B}T\right)$, which is derived from the Arrhenius equation. (

**b**) Corresponding activation energies.

**Figure 5.**The schematic plastic deformation map created in this work. The applied stress was normalized to the tensile strength. The coupled mechanism means the creep mechanism is coupled by dislocation creep and grain boundary creep.

**Figure 7.**(

**a**–

**d**) Snapshots of atomic-scale crystalline structures of model M1 at 100 ps in different creep processes. (Green: FCC; red: stacking fault; gray: other.) (

**a**) 500 K–0.4 ${R}_{\mathrm{m}}$–100 ps, (

**b**) 500 K–0.8 ${R}_{\mathrm{m}}$–100 ps, (

**c**) 1200 K–0.4 ${R}_{\mathrm{m}}$–100 ps, (

**d**) 1200 K–0.65 ${R}_{\mathrm{m}}$–100 ps.

**Figure 8.**Dislocation activities observed in dislocation creep regime. (

**a**) A dislocation jog as a dislocation moves through a stacking fault. (

**b**) The half plane of the dislocation line has jumped into a vacancy. (Red atoms: stacking faults; gray atoms: other; green lines: Shockley partial dislocations.)

**Figure 9.**(

**a**–

**c**) Snapshots of atomic-scale crystalline structures of model M1 at 1200 K and $0.4{R}_{\mathrm{m}}$ at different times in the creep process. The grain depicted in the half circle was moving out of sight during the creep process from 100 to 200 ps. (

**d**) The nearest neighbor atoms of two vacancies that are enlarged from (

**c**). For a clear illustration, the FCC atoms are deleted in (

**d**). (Green: FCC; red: stacking fault; gray: others.) (

**a**) 100 ps; (

**b**) 150 ps; (

**c**) 200 ps; (

**d**) two vacancies.

**Figure 10.**Log–log scaling plot of creep rate $\dot{\epsilon}$ over grain size d and the fit-curve at 800 K. The grain size exponents are $p=2.57$ at 0.7 ${R}_{\mathrm{m}}$ and $p=2.04$ at 0.8 ${R}_{\mathrm{m}}$, respectively.

Temperature | Bulk Modulus | Poisson’s Ratio | Young’s Modulus | Shear Modulus |
---|---|---|---|---|

T [K] | K [GPa] | $\mathsf{\mu}$ [-] | E [GPa] | G [GPa] |

500 | 162.754 | 0.379 | 223.330 | 95.427 |

800 | 150.985 | 0.379 | 207.814 | 88.310 |

1200 | 135.164 | 0.381 | 189.529 | 77.88 |

Model | Number of Grains N | Averaged Grain Size d [nm] |
---|---|---|

M1 | 30 | 19.96 |

M2 | 25 | 21.22 |

M3 | 20 | 22.85 |

M4 | 15 | 25.15 |

M5 | 10 | 28.79 |

500 K | 600 K | 700 K | 800 K | 900 K | 1000 K | 1100 K | 1200 K | |
---|---|---|---|---|---|---|---|---|

low $\sigma $ | 2.6 | 2.3 | 3.0 | 3.3 | 3.6 | 3.1 | 1.5 | 4.8 |

high $\sigma $ | 13.8 | 13.2 | 13.0 | 10.0 | 8.3 | 8.4 | 7.5 | 6.8 |

**Table 4.**Comparison of two creep processes. The stacking fault ratio represents how many are atoms with an HCP structure compared with the total number of atoms in the model.

Temperature [K] | 800 | 1200 |

stress level | 0.65 ${R}_{\mathrm{m}}$ | 0.4 ${R}_{\mathrm{m}}$ |

stress [GPa] | 1.76 | 0.90 |

creep rate [$1/s$] | $3.98\times {10}^{7}$ | $2.26\times {10}^{7}$ |

stress exponent n | 10.0 | 4.8 |

stacking fault ratio at 100 ps | $4.3\%$ | $2.4\%$ |

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**MDPI and ACS Style**

Xu, X.; Binkele, P.; Verestek, W.; Schmauder, S.
Molecular Dynamics Simulation of High-Temperature Creep Behavior of Nickel Polycrystalline Nanopillars. *Molecules* **2021**, *26*, 2606.
https://doi.org/10.3390/molecules26092606

**AMA Style**

Xu X, Binkele P, Verestek W, Schmauder S.
Molecular Dynamics Simulation of High-Temperature Creep Behavior of Nickel Polycrystalline Nanopillars. *Molecules*. 2021; 26(9):2606.
https://doi.org/10.3390/molecules26092606

**Chicago/Turabian Style**

Xu, Xiang, Peter Binkele, Wolfgang Verestek, and Siegfried Schmauder.
2021. "Molecular Dynamics Simulation of High-Temperature Creep Behavior of Nickel Polycrystalline Nanopillars" *Molecules* 26, no. 9: 2606.
https://doi.org/10.3390/molecules26092606