# Experimental and Molecular Dynamic Study of Grain Refinement and Dislocation Substructure Evolution in HSLA and IF Steels after Severe Plastic Deformation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{A}= 500 °C and annealed for t

_{A}= 1200 s in order to stabilize highly energetic ultrafine grains. This level of temperature, in the case of steel, accelerates the dislocation substructure rearrangements and process of the continuous recrystallization (in-situ) due to, generally speaking, increased ability of the dislocations to the movement.

^{i}and slip plane normal direction z

^{i}, and ρ

^{i}is the scalar dislocation density of dislocation i. The dislocation density tensor method considers both edge and screw dislocations. Other dislocation structures that are made consist of the dislocation density tensor, e.g., dislocation dipole is treated as statistically stored dislocations. The maximum misorientation between neighboring points should be entered and the threshold value was 5°, larger misorientations were not considered in the GDNs density calculation. The presented method was used as an automated calculation in the TSL OIM Analysis software (version 4.1, EDAX, USA).

## 3. Results and Discussion

## 4. Modeling

_{i}—mass, a

_{i}—accelerations, x

_{i}—displacements, V

_{i}—velocities, F

_{i}—forces, t—time.

_{i}acting on the i-th atom is thus determined using interatomic potential, which is a function of all atoms’ positions and its value denotes potential energy of the whole system. In order to obtain the value of the force, the potential should be differentiated after the position of the given atom. The model defined in this way allows for the description of the motion of atoms, and thus the observation of changes taking place in the tested system, and enables the determination of the macroscopic parameters of the material.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Stefanska-Kadziela, M.; Majta, J.; Muszka, K. Strain rate dependency of the dislocation substructure formation in HSLA and IF steels. In Proceedings of the International conference on Microalloyed Steels, in Processings Microstructure, Properties and Performance, Pittsburgh, PA, USA, 16–19 July 2006; pp. 181–192. [Google Scholar]
- Muszka, K.; Majta, J.; Hodgson, P.D. Modeling of the mechanical behavior of nanostructured HSLA steels. ISIJ Inter
**2007**, 47, 1221–1227. [Google Scholar] [CrossRef] - Majta, J.; Muszka, K. Mechanical properties of ultrafine-grained HSLA and Ti-IF steels. Mater. Sci. Eng. A
**2007**, 464, 186–191. [Google Scholar] [CrossRef] - Papanikolaou, M.; Salonitis, K. Contact stiffness effects on nanoscale high-speed grinding: A molecular dynamics approach. Appl. Surf. Sci.
**2019**, 493, 212–224. [Google Scholar] [CrossRef] - Fu, T.; Peng, X.; Zhao, Y.; Sun, R.; Weng, S.; Feng, C.; Wang, Z. Molecular dynamics simulation of TiN (001) thin films under indentation. Ceram. Int.
**2015**, 41, 14078–14086. [Google Scholar] [CrossRef] - Povarnitsyn, M.E.; Fokin, V.B.; Levashov, P.R.; Itina, T.E. Molecular dynamics simulation of subpicosecond double-pulse laser ablation of metals. Phys. Rev. B
**2015**, 92, 174104. [Google Scholar] [CrossRef] - Benkabou, F.; Aourag, H.; Certier, M. Atomistic study of zinc-blende CdS, CdSe, ZnS, and ZnSe from molecular dynamics. Mater. Chem. Phys.
**2000**, 66, 10–16. [Google Scholar] [CrossRef] - Curtin, W.A.; Miller, R.E. Atomistic/continuum coupling in computational materials science. Modell. Simul. Mater. Sci. Eng.
**2003**, 11, R33–R68. [Google Scholar] [CrossRef] - Schuh, C.A.; Lund, A.C. Atomistic basis for the plastic yield criterion of metallic glass. Nat. Mater.
**2003**, 2, 449–452. [Google Scholar] [CrossRef] [PubMed] - Gunsteren, W.F.; Berendsen, H.J.C. Computer simulation of molecular dynamics: Methodology, applications, and perspectives in chemistry. Angew. Chem. Int. Ed. Engl.
**1990**, 29, 992–1023. [Google Scholar] [CrossRef] - Gunsteren, W.F.; Berendsen, H.J.C. Algorithms for macromolecular dynamics and constraint dynamics. Mol. Phys.
**1977**, 34, 1311–1327. [Google Scholar] [CrossRef] - Chen, W.C.; Ferguson, D.; Ferguson, H.S.; Mishra, R.S.; Jin, Z. Development of Ultrafine Grained Materials Using The MAXStrain® Technology. Mater. Sci. Forum
**2001**, 357–359, 425–430. [Google Scholar] [CrossRef] - Calcagnotto, M.; Ponge, D.; Demir, E.; Raabe, D. Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD. Mater. Sci. Eng. A
**2010**, 527, 2738–2746. [Google Scholar] [CrossRef] - Ruggles, T.J.; Fullwood, D.T. Estimations of bulk geometrically necessary dislocation density using high resolution EBSD. Ultramicroscopy
**2013**, 133, 8–15. [Google Scholar] [CrossRef] [PubMed] - Field, D.P.; Trivedi, P.B.; Wright, S.I.; Kumar, M. Analysis of local orientation gradients in deformed single crystals. Ultramicroscopy
**2005**, 103, 33–39. [Google Scholar] [CrossRef] [PubMed] - Daw, M.S.; Baskes, M.I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B
**1984**, 29, 6443–6453. [Google Scholar] [CrossRef][Green Version] - Hirel, P. Atomsk: A tool for manipulating and converting atomic data files. Comput. Phys. Commun.
**2015**, 197, 212–219. [Google Scholar] [CrossRef] - Doong, S.H. Deformation mechanisms of metals under complex nonproportinal cyclic loadings. In Proceedings of the International Conference on Multiaxial Fatigue and Fracture 3, Stuttgart, Germany, 3–6 April 1989; Volume 52a, pp. 1–20. [Google Scholar]
- Lisiecka-Graca, P.; Kwiecien, M.; Madej, L.; Muszka, K.; Majta, J.; Wynne, B.P. Controlling deformation inhomogeneity in the Accumulative Angular Drawing Process assisted by constitutive and multiscale numerical modelling. Comp. Meth. Mater. Sci.
**2019**, 19, 113–121. [Google Scholar]

**Figure 1.**Scheme of the MaxStrain experiment (

**a**); specimen after deformation (

**b**); positions of the EBSD and TEM studies in the specimens deformed with the MaxStrain system (

**c**).

**Figure 2.**TEM micrographs (grayscale) and EBSD (Euler angle distribution color maps) results for HSLA steel deformed with total strains of 2 (

**a,b**), 5 (

**c,d**), 7 (

**e,f**), 10 (

**g,h**), 15 (

**i,j**) and 20 (

**k,l**). Black lines—high-angle grain boundaries (HABs); red lines—low-angle grain boundaries (LABs).

**Figure 3.**Kernel average misorientation (KAM) distribution maps in HSLA steel specimens deformed with total strains of 2 (

**a**), 5 (

**b**), 7 (

**c**), 10 (

**d**), 15 (

**e**) and 20 (

**f**).

**Figure 4.**Geometrically necessary dislocations’ distribution maps in IF (

**a,c**) and HSLA (

**b,d**) steel specimens deformed with total strains of 5 (

**a,b**) and 20 (

**c,d**).

**Figure 6.**MD model setup. (

**a**) Top view of the cubic unit cell 400 × 400 × 400 Å with three ferrite grains and periodic boundary conditions; (

**b**) spherical particle of niobium nitride inserted into the cubic cell.

**Figure 7.**Atomic rearrangement (displacements) after the initial stage of compression in low- (

**a,c**) and high-misorientation (

**b,d**) grains of the unalloyed (

**a,b**) and alloyed (

**c,d**) system.

**Figure 8.**Mises stress distributions after compression in low- (

**a,c**) and high-misorientation (

**b,d**) grains of the unalloyed (

**a,b**) and alloyed (

**c,d**) system.

**Figure 9.**Evolution of defects during compression of grains with LABs (arrow indicates compression direction).

**Figure 10.**Evolution of defects during compression of grains with HABs (arrow indicates compression direction).

Steel | C | Mn | Si | Al | Nb | Ti | Fe |
---|---|---|---|---|---|---|---|

HSLA | 0.07 | 1.36 | 0.27 | 0.02 | 0.067 | 0.031 | Bal. |

IF | 0.0022 | 0.11 | 0.009 | 0.037 | - | 0.073 | Bal. |

MD Scheme | Grain 1 (Blue) Orientation | Grain 2 (Gray) Orientation | Grain 3 (Red) Orientation |
---|---|---|---|

Low-angle grain boundaries/solid solution (LS) | 0°; 0°; 0° | 1°; 2°; 1° | −1°; −2°; −1° |

Low-angle grain boundaries/with precipitation (LP) | |||

High-angle grain boundaries/solid solution (HS) High-angle grain boundaries/with precipation (HP) | 0°; 0°; 0° | 15°; 18°; 15° | 15°; 18°; 15° |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Muszka, K.; Zych, D.; Lisiecka-Graca, P.; Madej, L.; Majta, J. Experimental and Molecular Dynamic Study of Grain Refinement and Dislocation Substructure Evolution in HSLA and IF Steels after Severe Plastic Deformation. *Metals* **2020**, *10*, 1122.
https://doi.org/10.3390/met10091122

**AMA Style**

Muszka K, Zych D, Lisiecka-Graca P, Madej L, Majta J. Experimental and Molecular Dynamic Study of Grain Refinement and Dislocation Substructure Evolution in HSLA and IF Steels after Severe Plastic Deformation. *Metals*. 2020; 10(9):1122.
https://doi.org/10.3390/met10091122

**Chicago/Turabian Style**

Muszka, Krzysztof, Dawid Zych, Paulina Lisiecka-Graca, Lukasz Madej, and Janusz Majta. 2020. "Experimental and Molecular Dynamic Study of Grain Refinement and Dislocation Substructure Evolution in HSLA and IF Steels after Severe Plastic Deformation" *Metals* 10, no. 9: 1122.
https://doi.org/10.3390/met10091122