# Effect of Structural Heterogeneity of 17Mn1Si Steel on the Temperature Dependence of Impact Deformation and Fracture

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## Abstract

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## 1. Introduction

## 2. Experimental Procedure

## 3. Theoretical Procedure

- The stress ${\varsigma}_{ik}^{n-1}$ at the interface boundary of the i-th element and its k-th neighbor at the (n − 1)-th time step is calculated as the difference of hydrostatic pressures acting from each element of the considered pair:$${\varsigma}_{ik}^{n-1}={p}_{k}^{n-1}-{p}_{i}^{n-1}.$$
- A relation analogous to the Newtonian viscous flow assuming he proportionality between the force and velocity [3] is used to calculate the average velocity of material points ${v}_{ik}^{n}$ moving through a virtual boundary between fixed elements of space under the action of stress ${\varsigma}_{ik}^{n-1}$:$${v}_{ik}^{n}=-{\aleph}_{ik}\cdot {\varsigma}_{ik}^{n-1}.$$$${\aleph}_{ik}={\left({\aleph}_{0}\right)}_{ik}\cdot {\left(\frac{{\eta}_{i}^{n-1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\eta}_{k}^{n-1}}{{N}_{i}^{n}+{N}_{k}^{n}}\right)}^{{\eta}_{i}^{n-1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\eta}_{k}^{n-1}}{e}^{-\frac{{\Im}_{ik}}{{k}_{B}{T}_{ik}}}.$$$${\left({\aleph}_{0}\right)}_{ik}=\frac{c}{{Y}_{i}{Y}_{k}}{e}^{-\frac{{({Y}_{i}-{Y}_{k})}^{2}}{{Y}_{i}{Y}_{k}}},$$$${\Im}_{ik}=\{\begin{array}{cc}{\gamma}_{HAGB}\frac{\Delta ({\overrightarrow{\theta}}_{i},\text{\hspace{0.17em}}{\overrightarrow{\theta}}_{k})}{{\theta}_{HAGB}}\left(1-\mathrm{ln}\frac{\Delta ({\overrightarrow{\theta}}_{i},\text{\hspace{0.17em}}{\overrightarrow{\theta}}_{k})}{{\theta}_{HAGB}}\right),& \text{\hspace{0.17em}}\Delta ({\overrightarrow{\theta}}_{i},\text{\hspace{0.17em}}{\overrightarrow{\theta}}_{k})>0,\\ 0,& \Delta ({\overrightarrow{\theta}}_{i},\text{\hspace{0.17em}}{\overrightarrow{\theta}}_{k})=0\hfill \end{array},$$$$\frac{{\Delta \mathsf{\Lambda}}_{ik}^{n}}{{\mathsf{\Lambda}}_{c}}=\Delta {\beta}_{ik}^{n}=\frac{{v}_{ik}^{n-1}\Delta \tau}{{l}_{c}},$$$$\Delta {E}_{ik}^{n}=\Delta {\beta}_{ik}^{n}{\varsigma}_{ik}^{n-1}\text{\hspace{0.17em}}{\mathsf{\Lambda}}_{c}.$$
- The total relative volume change ($\Delta {\beta}_{i}^{n}$) and the mechanical energy change ($\Delta {E}_{i}^{n}$) of the i-th element are found as a result of its interaction with all of nearest neighbors:$$\Delta {\beta}_{i}^{n}=\frac{{\Delta \mathsf{\Lambda}}_{i}^{n}}{{\mathsf{\Lambda}}_{c}}={\displaystyle \sum _{k=1}^{K}\frac{{\Delta \mathsf{\Lambda}}_{ik}^{n}}{{\mathsf{\Lambda}}_{c}}}={\displaystyle \sum _{k=1}^{K}\Delta {\beta}_{ik}^{n}},$$$$\Delta {E}_{i}^{n}={\displaystyle \sum _{k=1}^{K}\Delta {E}_{ik}^{n}}.$$

_{G}is the total number of grains. At the same time, the following conditions must be satisfied at the zero time step:

## 4. Results and Discussion

#### 4.1. Simulation of Impact Loading Meso-Dynamics at Different Temperatures

^{−1}during the first 500 μs and then extended at the same rate during the next 500 μs (Figure 3b,d). There is no energy exchange through other boundaries.

#### 4.2. Fracture Micromechanisms

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustrations: (

**a**) polycrystalline specimen as a cellular automaton; (

**b**) grains with crystal lattice; (

**c**) neighboring grains with different lattice orientations; (

**d**) calculation scheme for the angular velocity of material microrotation in the active element of the cellular automaton.

**Figure 2.**(

**a**,

**b**) Optical images of 17Mn1Si steel microstructure in the as-delivered state, (

**c**) impact loading curves in the “load–displacement” coordinates for the specimens with the V-notch tested at different temperatures shown in the legend, (

**d**) dependence of the maximum contraction ratio of specimens λ (%) in the crack growth region on the test temperature T, °C for specimens with different concentrator shapes

**Figure 3.**Schematic of the specimen or simulated mesoscopic volume (

**a**); deformation scheme (

**b**); position of the simulated specimen (plane A) in the simulated system (

**c**); and time—load dependence (

**d**). E in (

**c**) means residual cross section in the notch tip vicinity.

**Figure 4.**Specific elastic energy of specimens vs. time (

**a**); total strain vs. test temperature (500 µm) (

**b**); average angular velocity of microrotations vs. time (

**c**); and fraction of microrotation energy in the total elastic energy supplied vs. test temperature (500 µm) (

**d**). The legends show the temperatures T in °C.

**Figure 5.**Specific elastic energy distribution on specimen faces at different temperatures at 500 μs after the beginning of loading. (

**a**) −60 °C; (

**b**) −20 °C; (

**c**) 20 °C; (

**d**) color legend.

**Figure 6.**Specific rotation energy distribution on specimen faces at different temperatures at 500 μs after the beginning of loading. (

**a**) −60 °C; (

**b**) −20 °C; (

**c**) 20 °C; (

**d**) color legend.

**Figure 7.**Relative rotation energy distribution on specimen faces at different temperatures at 500 μs after the beginning of loading. (

**a**) −60 °C; (

**b**) −20 °C; (

**c**) 20 °C; (

**d**) color legend.

**Figure 8.**Distribution of the accumulated angle of local material rotation ${\gamma}_{\perp}=\sqrt{{\gamma}_{x}^{2}+{\gamma}_{z}^{2}}$ on specimen faces at different temperatures at 500 μs after the start of loading: (

**a**) −60 °C; (

**b**) −20 °C; (

**c**) 20 °C; (

**d**) color legend.

**Figure 9.**Scanning Electron Microscope (SEM) images of the fracture surface of impact bending specimens tested at different temperatures. (

**a**) T = 20 °C; (

**b**) T = −20 °C; (

**c**) T = −60 °C.

**Table 1.**Impact toughness and maximum contraction ratio of specimens λ (%) in the crack growth region.

T, °C | −60 | −40 | −20 | 0 | 20 |
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KCV, J/cm^{2} | 9.3 ± 2 | 20 ± 3 | 46 ± 9 | 60 ± 10 | 73.3 ± 12 |

λ, % | 0.03 ± 0.005 | 0.04 ± 0.006 | 0.06 ± 0.005 | 0.09 ± 0.007 | 0.11 ± 0.006 |

Temperature, K (°C) | 213.2 (−60) | 233.2 (−40) | 253.2 (−20) | 273.2 (0) | 293.2 (20) |
---|---|---|---|---|---|

k_{diss} | 250 | 500 | 1000 | 2000 | 4000 |

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**MDPI and ACS Style**

Moiseenko, D.; Maruschak, P.; Panin, S.; Maksimov, P.; Vlasov, I.; Berto, F.; Schmauder, S.; Vinogradov, A. Effect of Structural Heterogeneity of 17Mn1Si Steel on the Temperature Dependence of Impact Deformation and Fracture. *Metals* **2017**, *7*, 280.
https://doi.org/10.3390/met7070280

**AMA Style**

Moiseenko D, Maruschak P, Panin S, Maksimov P, Vlasov I, Berto F, Schmauder S, Vinogradov A. Effect of Structural Heterogeneity of 17Mn1Si Steel on the Temperature Dependence of Impact Deformation and Fracture. *Metals*. 2017; 7(7):280.
https://doi.org/10.3390/met7070280

**Chicago/Turabian Style**

Moiseenko, Dmitry, Pavlo Maruschak, Sergey Panin, Pavel Maksimov, Ilya Vlasov, Filippo Berto, Siegfried Schmauder, and Alexey Vinogradov. 2017. "Effect of Structural Heterogeneity of 17Mn1Si Steel on the Temperature Dependence of Impact Deformation and Fracture" *Metals* 7, no. 7: 280.
https://doi.org/10.3390/met7070280