# The Effect of Impact Load on the Atomistic Scale Fracture Behavior of Nanocrystalline bcc Iron

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Model and Methods

_{X}× L

_{Y}× L

_{Z}dimensional size of 60 nm × 60 nm × 30 nm and 9,197,099 iron atoms. It is very isotropic and has a good inverse Hall–Petch relationship with nanocrystalline irons with average grain diameters of 5 nm and 10 nm [34]. After developing the nanocrystalline model, the processes of minimization, equilibration, and stretching simulation are performed in a large-scale atomic/molecular massively parallel simulator [38]. These processes are based on the precise description of the interactions between iron atoms. In this work, the embedded-atom potential developed by Mendelev et al. [39] is applied. During minimization, the conjugate gradient algorithm is used. The energy and force tolerances are 10

^{−15}, and the maximum number of force and energy evaluations is 10

^{4}. Due to the large dimensional size, minimization process is performed many times until the model state parameters remain unchanged. After minimization, an edge crack with front parallel to Z direction is created at the left of the model by directly deleting atoms, and its length in X direction is 20 nm. In Y direction, the crack is the same distance from the top and bottom of the model, as shown in Figure 1. Then, atomic initial velocities are set by a random number generator with the specified seed at the temperature of 1 K to avoid thermal effect. Based on atomic locations at the end of minimization and atomic initial velocities, the cracked model is fully equilibrated under microcanonical ensemble, where atomic velocities are explicitly rescaled to remain at a temperature of 1 K. After equilibration, the cracked model is stretched along Y direction by adding force on several layer atoms on the top and bottom under microcanonical ensemble, as shown in Figure 1a. In the directions of X and Y, free boundaries are applied to stretch the cracked model freely. In the directions of Z, periodic boundaries are applied to avoid the effect of extra surface on crack propagation. Additionally, the application of periodic boundaries puts the cracked model in a plane strain state. During the processes of equilibration and stretching simulation, velocity Verlet algorithm [40] is used to solve Newton’s equations, and timestep is 10

^{−3}ps. To identify the effect of loading rate on crack propagation in nanocrystalline bcc iron, the stretch process is performed five times, and the growth rates of stretch stress are 6.65 × 10

^{−2}Gpa/ps, 1.33 × 10

^{−1}Gpa/ps, 2.00 × 10

^{−1}Gpa/ps, 2.66 × 10

^{−1}Gpa/ps, and 3.33 × 10

^{−1}Gpa/ps, respectively. As shown in Figure 1b–d, the distribution of grain boundaries and crystal orientation of grains are very different on different cross-sections normal to Z direction. Hence, the crack propagation behaviors on different cross-sections are very different. Discussion on the loading rate effect needs to consider crack propagation behaviors on different cross-sections.

## 3. Results and Discussions

#### 3.1. Engineering Stress–Strain Behaviors

^{−1}GPa/ps are very different from those under loading rates higher than 2.00 × 10

^{−1}GPa/ps. When the loading rate is lower than 2.00 × 10

^{−1}GPa/ps, secondary hardening can be observed clearly. However, when the loading rate is higher than 2.00 × 10

^{−1}GPa/ps, secondary hardening cannot be observed. Therefore, the mechanisms of plastic deformation under loading rates lower than 2.00 × 10

^{−1}GPa/ps may be different from those under loading rates higher than 2.00 × 10

^{−1}GPa/ps. The different plastic deformation mechanisms can lead to the obvious difference in fracture behavior of the cracked nanocrystalline model.

#### 3.2. Crack Propagation Behaviors

^{−1}GPa/ps, crack propagation dominates the stress–strain behavior. The obvious ductile transgranular propagation can result in secondary hardening. When the loading rate is higher than 2.00 × 10

^{−1}GPa/ps, grain boundary activities hinder crack propagation and dominate the stress–strain behavior. The fracture behavior of nanocrystalline bcc iron keeps high toughness due to the obvious grain boundary activities. Hence, secondary hardening cannot be observed.

#### 3.3. Ductile–Brittle Characteristics

^{−1}GPa/ps is 15.3 times that under the loading rate of 6.65 × 10

^{−2}GPa/ps, while the plastic atom number under the loading rate of 3.33 × 10

^{−1}GPa/ps is 30.74 times that under the loading rate of 6.65 × 10

^{−2}GPa/ps. With an increase in loading rate, the plastic atom number grows faster than the new surface atom number.

_{p}can be very large in the initial stage of crack cleavage because plastic behaviors can be generated before cleavage on most cross-sections. To avoid this situation, the term of G

_{p}can be written as

^{2}. Similarly, the term of G

_{s}can be computed as

_{d}increases significantly with crack growth at this stage, as shown by the portion designated by PQ in Figure 5. When the loading rate is lower than 2.00 × 10

^{−1}GPa/ps, crack propagation behavior is more obvious than grain boundary activities. The increase in loading rate can lead to an obvious increase in the growth rate of the required energy G

_{d}. With the loading rate further increasing, grain boundary activities become more and more obvious. As a result, the growth rate of the required energy G

_{d}cannot increase significantly, with the loading rate further increasing when the loading rate is more than 2.00 × 10

^{−1}GPa/ps. Out of the stage designated by PQ, intergranular crack propagation occurs again on some cross-sections, and it will accelerate crack ductile growth on other cross-sections by intergranular decohesion. With the loading rate increasing, the intergranular decohesion weakens. The difference in the required energy G

_{d}under different loading rates becomes obvious. When crack growth length is 250 Å, the required energy G

_{d}under the loading rate of 3.33 × 10

^{−1}GPa/ps is almost 2.62 times that under the loading rate of 6.65 × 10

^{−2}GPa/ps and almost 4.7 times the Griffith energy release rate. In this work, the Griffith energy release rate is measured as 3.58 J/m

^{2}. The fracture with high required energy G

_{d}has a high ductility. The increase in loading rate can significantly increase the fracture ductility of nanocrystalline bcc iron.

## 4. Conclusions

- (1)
- The engineering stress–strain behaviors of cracked nanocrystalline iron are very disparate under different loading rates. On the one hand, the ultimate tensile stress increases with an increase in loading rate in a weak, nonlinear way. On the other hand, plastic deformation will cause secondary hardening of the stress–strain behavior at a low loading rate but not at a high loading rate.
- (2)
- Ductile–brittle characteristics of crack propagation on different cross-sections are very unique, and fast brittle cleavage on some cross-sections can accelerate ductile propagation on their adjacent cross-sections through intergranular decohesion. With the loading rate increasing, intergranular decohesion weakens, and more plastic behaviors are generated by grain boundary activities. The obvious grain boundary activities result in the formation of microvoids at the position far away from the crack tip and hinder crack propagation. The differences in crack propagation behavior and grain boundary activity under different loading rates determine whether secondary hardening occurs or not.
- (3)
- The promoted grain boundary activities by the increase in loading rate cause an increase in the threshold energy for crack cleavage and enhance the resistance to the fracture of nanocrystalline bcc iron. After crack cleavage, both the new surface atom number and the plastic atom number grow with an increase in loading rate in a strong, nonlinear way, but the plastic atom number grows faster than the new surface atom number. The increase in loading rate can significantly increase the fracture ductility of nanocrystalline bcc iron.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Nanocrystalline bcc iron model. (

**a**) shows a 3D view, where colors are used to distinguish different grains. (

**b**–

**d**) show the distributions of grain boundaries and atoms on different cross-sections (A, B, and C) normal to Z direction, where the Z values of atoms on cross-section A are between 14.78 and 15.22 nm. Those on cross-section B are between 16.78 and 17.22 nm, and those on cross-section C are between 23.78 and 24.22 nm. In (

**b**–

**d**), green atoms have bcc crystal structure and are located inside the grains; pink ones are located at grain boundaries, and yellow ones are located at the surfaces of crack and model.

**Figure 2.**Engineering stress–strain behaviors under different loading rates, where (

**a**) is the stress–strain curves and (

**b**) is the maximum tensile stresses. The dashed lines in (

**b**) are drawn linearly based on two adjacent points.

**Figure 3.**Crack propagation behaviors in nanocrystalline bcc iron under tensile stress with different growth rates, where cross-sections A, B, and C are atomic planes that contain points A, B, and C in 3D view, respectively. In the figure of 3D crack surface, the color gradient is on the basis of X coordinate value of iron atom. In the figures that depict behaviors on cross-sections A, B, and C, green and blue atoms have bcc and fcc crystal structures, respectively; pink ones are located at grain boundaries and dislocation cores, and yellow atoms are located at the surfaces of crack and voids.

**Figure 4.**Variations of (

**a**) new surface atom number and (

**b**) plastic atom number during crack propagation under different loading rates.

**Figure 5.**Variations of the energy required to form a unit area of crack unilateral surface with crack growth length under different loading rates.

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**MDPI and ACS Style**

Zhao, Z.; Wang, Z.; Bie, Y.; Liu, X.; Wei, Y.
The Effect of Impact Load on the Atomistic Scale Fracture Behavior of Nanocrystalline bcc Iron. *Nanomaterials* **2024**, *14*, 370.
https://doi.org/10.3390/nano14040370

**AMA Style**

Zhao Z, Wang Z, Bie Y, Liu X, Wei Y.
The Effect of Impact Load on the Atomistic Scale Fracture Behavior of Nanocrystalline bcc Iron. *Nanomaterials*. 2024; 14(4):370.
https://doi.org/10.3390/nano14040370

**Chicago/Turabian Style**

Zhao, Zhifu, Zhen Wang, Yehui Bie, Xiaoming Liu, and Yueguang Wei.
2024. "The Effect of Impact Load on the Atomistic Scale Fracture Behavior of Nanocrystalline bcc Iron" *Nanomaterials* 14, no. 4: 370.
https://doi.org/10.3390/nano14040370