# Studying Plastic Deformation Mechanism in β-Ti-Nb Alloys by Molecular Dynamic Simulations

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## Abstract

**:**

## 1. Introduction

## 2. Computational Method

#### 2.1. FS Potential Function

#### 2.2. First-Principles Calculations

^{−3}eV/Å.

#### 2.3. Molecular Dynamics (MD)

## 3. Results

#### 3.1. Potential Function Validation

^{−2}, indicating reasonable agreement with the DFT-calculated theoretical values. Furthermore, the trend of unstable stacking fault energies with changing composition was accurately reproduced. The elastic constants of alloys with three different compositions were also calculated, as shown in Table 3. These values were compared to other theoretical values from DFT calculations, and the errors were within acceptable ranges.

#### 3.2. Analysis of Tensile Behavior

#### ω-Phase Transformation

#### 3.3. The Influence of Computational Cell Size on the Tensile Mechanical Properties of Ti-Nb Alloys

#### 3.4. The Influence of Temperature on the Tensile Mechanical Properties of Ti-Nb Alloys

#### 3.5. The Influence of Composition Variation on the Tensile Mechanical Properties of Ti-Nb Alloy

#### Dislocation and Twinning

#### 3.6. The Influence of Strain Rate on the Tensile Mechanical Properties of Ti-Nb Alloy

^{−1}, a significantly wider transition range is observed. When the tensile strain rate of the alloy is 0.0001 ps

^{−1}, the quantity of twins is exceedingly limited, as shown in Figure 11b. When the strain reaches 0.125, the twins disappear, and the deformation mechanism completely changes to a dislocation slip. Moreover, the dislocation slip continues in the following deformation.

^{−1}, the microstructure within the transformation interval exhibits greater disorder, characterized by the significant presence of twinning, point defects, and dislocations. The synergistic effect of various deformation mechanisms significantly improves the plasticity of the alloy.

## 4. Conclusions

- The overall deformation process of Ti-Nb alloys involves point-defect generation, followed by twinning and ω-phase transition, and ultimately, dislocation slip occurs. With the increase in the simulation model’s size, the deformed twins’ stability increases, and the strength of the material reduces. In addition, increasing temperature enhances the plasticity and reduces the strength of the material, while increasing composition has the opposite effect on the deformation.
- The elevated stresses resulting from molecular dynamics at higher strain rates cause the <111>{112} slip system to become more pronounced compared to experimental conditions. The interfacial ω-phase induced by the <111>{112} slip system also makes it easier to pass through the energy barrier of the phase transition, making its formation in the matrix easier.
- The predominant deformation mechanisms in Ti-Nb alloys involve twinning and dislocation slip, exhibiting a certain degree of competitiveness. At low Nb content, the number of twins increases with the increase in Nb content, making twinning the dominant mechanism in the overall deformation process. At high Nb content, dislocation slip is still active, but the addition of β-stability elements suppresses twinning deformation. The proportion of twinning decreases, leading to a shift in the plastic deformation mode from twinning to dislocation slip.
- At low strain rates, the twins disappear at a slight strain, while higher strain rates result in an increased number of twins. Moreover, the transition strain interval from stacking faults to twin dislocation slip significantly increases. Various deformation mechanisms work synergistically to enhance the material’s plasticity.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Tensile behavior of Ti-25Nb (at.%) alloy at 300 K. (where blue atoms represent BCC structures, green atoms represent FCC structures, and white atoms represent other structures).

**Figure 4.**Microstructures of the stacking fault structure viewed from the [1$\overline{1}$0] direction, where (

**a**): Microstructure at 0.04 strain; (

**b**): Microstructure at 0.092 strain (ultimate); (

**c**): Microstructure at 0.118 strain; (

**d**): Magnified view of the stacking fault structure, where b = 1/2[11$\overline{1}$].

**Figure 5.**Diagram of the twinning plastic deformation process, where (

**a**): Stacking fault and twinning transition under tensile loading; (

**b**): Microstructure of the twinning region; (

**c**): Twinning formation process as viewed from [1$\overline{1}$0] direction.

**Figure 6.**(

**a**) Twin boundary diagram in the [111] direction; (

**b**) Crystal twin boundary diagram in the [1$\overline{1}$0] direction; (

**c**) BCC atom arrangement in the [111] direction; (

**d**) ω-phase atom arrangement in the [0001] direction; (

**e**) BCC atom arrangement in the [1$\overline{1}$0] direction.

**Figure 7.**Tensile behavior of Ti-25Nb (at.%) alloy at different computational cell size, where: (

**a**) Stress–strain curves during tensile loading at 300 K temperature at 0.001/ps strain rate; (

**b**) Microstructure of 32,000 atoms cell size at 0.124 and 0.133 strain; (

**c**) Microstructure of 256,000 atoms cell size at 0.124 and 0.133 strain; (

**d**) Microstructure of 2,048,000 atoms cell size at 0.124 and 0.133 strain. (where blue atoms represent BCC structures, green atoms represent FCC structures, red atoms represent HCP structures, and white atoms represent other structures).

**Figure 8.**Tensile behavior of Ti-25Nb (at.%) alloy at 0.001/ps at different temperatures, where: (

**a**) Stress–strain curves during tensile loading of Ti-25Nb (at.%) alloy; (

**b**) Microstructure at 200 K temperature at 0.113 and 0.117 strain; (

**c**) Microstructure at 300 K at 0.119 and 0.123 strain; (

**d**) Microstructure at 400 K temperature at 0.124 and 0.128 strain. (where blue atoms represent BCC structures, green atoms represent FCC structures, red atoms represent HCP structures, and white atoms represent other structures).

**Figure 9.**Tensile behavior of alloys at 300 K temperature at 0.001/ps strain rate, where: (

**a**) Stress–strain curve pictures of Ti-xNb (at.%) (x = 25, 30, 50, 75) alloys during tensile loading; (

**b**) Microstructure of Ti-25Nb (at.%) at 0.119 and 0.123 strain; (

**c**) Microstructure of Ti-50Nb (at.%) at 0.106 and 0.112 strain; (

**d**) Microstructure of Ti-75Nb (at.%) at 0.105 and 0.107 strain. (where blue atoms represent BCC structures, green atoms represent FCC structures, red atoms represent HCP structures, and white atoms represent other structures).

**Figure 10.**Statistical plots of the number of changes in dislocation density and twin fraction with alloy composition at 0.125 strain.

**Figure 11.**Tensile behavior of Ti-25Nb (at.%) alloy at 300 K at different strain rates, where: (

**a**) Tensile stress–strain curves of Ti-25Nb (at.%) alloy at strain rates of 0.0001 ps

^{−1}, 0.001 ps

^{−1}, 0.01 ps

^{−1}; (

**b**) Microstructures of 0.0001 ps

^{−1}strain rate at 0.116 and 0.125 strains; (

**c**) Microstructures of 0.001 ps

^{−1}strain rate at 0.125 and 0.2 strains; (

**d**) Microstructures of 0.01 ps

^{−1}strain rate at 0.175 and 0.2 strains. (where blue atoms represent BCC structures, green atoms represent FCC structures, red atoms represent HCP structures, and white atoms represent other structures).

**Table 1.**Lattice constants and cohesive energies of the alloys in Figure 2.

Ti4Nb12 | Ti8Nb8 | Ti10Nb6 | Ti12Nb4 | ||
---|---|---|---|---|---|

Lattice Constant/Å | MD (This work) | 3.317 | 3.324 | 3.278 | 3.265 |

DFT (This work) | 3.302 | 3.271 | 3.267 | 3.264 | |

[38] | 3.289 | 3.286 | |||

Cohesive Energy/eV | MD (This work) | −6.838 | −6.038 | −5.739 | −5.429 |

DFT (This work) | −6.554 | −6.185 | −6.020 | −5.855 |

γ_{us} on {110} (J m^{−2}) | γ_{us} on {112} (J m^{−2}) | |
---|---|---|

Ti-25Nb (at.%) | 0.408 | 0.381 |

DFT [37] | 0.307 | 0.296 |

Ti-50Nb (at.%) | 0.501 | 0.459 |

DFT [37] | 0.329 | 0.371 |

Ti-75Nb (at.%) | 0.581 | 0.531 |

DFT [37] | 0.494 | 0.534 |

Nb | 0.657 | 0.714 |

DFT [37] | 0.678 | 0.781 |

Content | Elastic Constant | This Work | [39] | [40] |
---|---|---|---|---|

Ti-25Nb (at.%) | C11 | 123.9 | 128.5 | 140 ± 11 |

C12 | 85.5 | 115.5 | 116 ± 13 | |

C44 | 51.7 | 14.9 | 34 ± 10 | |

B | 98.3 | 124 ± 13 | ||

G | 19.2 | 22 ± 13 | ||

Ti-50Nb (at.%) | C11 | 167.5 | 155.4 | 181 ± 9 |

C12 | 88.3 | 124.7 | 121 ± 2 | |

C44 | 52.2 | 12.8 | 31 ± 10 | |

B | 114.7 | 141 ± 9 | ||

G | 39.6 | 31 ± 10 | ||

Ti-75Nb (at.%) | C11 | 198.1 | 203.5 | 208 ± 3 |

C12 | 104.0 | 126.8 | 130 ± 4 | |

C44 | 43.7 | 21.3 | 15 ± 10 | |

B | 135.4 | 156 ± 4 | ||

G | 47.1 | 22 ± 10 |

**Table 4.**Twinning fraction at the strain of 0.124 in the alloy at different computational cell size.

Computational Cell Size | 32,000 atoms | 256,000 atoms | 2,048,000 atoms |
---|---|---|---|

Twinning fraction (%) | 0.109 | 0.252 | 0.263 |

**Table 5.**Percentage of atoms with other structures at the strain of 0.1 in the alloy at various temperatures.

Temperature | 200 K | 300 K | 400 K |
---|---|---|---|

Other structure concentration (%) | 3.1 | 7.9 | 15.1 |

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**MDPI and ACS Style**

Wang, H.; Huang, B.; Hu, W.; Huang, J.
Studying Plastic Deformation Mechanism in β-Ti-Nb Alloys by Molecular Dynamic Simulations. *Metals* **2024**, *14*, 318.
https://doi.org/10.3390/met14030318

**AMA Style**

Wang H, Huang B, Hu W, Huang J.
Studying Plastic Deformation Mechanism in β-Ti-Nb Alloys by Molecular Dynamic Simulations. *Metals*. 2024; 14(3):318.
https://doi.org/10.3390/met14030318

**Chicago/Turabian Style**

Wang, Hongbo, Bowen Huang, Wangyu Hu, and Jian Huang.
2024. "Studying Plastic Deformation Mechanism in β-Ti-Nb Alloys by Molecular Dynamic Simulations" *Metals* 14, no. 3: 318.
https://doi.org/10.3390/met14030318