# Determination of Grain Growth Kinetics of S960MC Steel

^{1}

^{2}

^{*}

## Abstract

**:**

_{0}are determined. Knowing these values is important for numerical predictions of austenitic grain size in the HAZ. Based on these predictions, the changes in yield strength, ductility, toughness, and fatigue strength can be estimated.

## 1. Introduction

_{y}(MPa·mm

^{1/2}) is a coefficient expressing the effect of ferritic grain size on the increase in yield strength and d

_{α}(mm) is the mean ferritic grain size. As a result, during the manufacturing process, every effort is taken to minimize the grain size to the smallest possible size. The TMCP achieves this structure by combining controlled rolling and cooling with the precipitation of (V, Nb) (C, N)-type dispersed precipitates [2,3,4].

_{0}is the initial grain diameter, t is the soaking time at a given temperature, K and K

_{0}are proportional constants depending on the temperature T and the activation energy Q required for grain growth, and R is the universal gas constant.

_{0}and the value of the activation energy required for grain growth Q in S960MC steel have not yet been published, the aim of this work is to determine these constants. Knowing these constants is essential for the accurate determination of grain size by computing or by numerical simulation (for example, in Sysweld software). Due to the nature of the material and significant differences in microstructure and chemical composition, it is not possible to replace these constants with those from related materials.

## 2. Materials and Methods

#### 2.1. Experimental Material

#### 2.2. Determination of Activation Energy Q and Kinetic Constant of Grain Growth K

_{mean}) was determined as the square of the mean austenitic grain size (D). A linear curve was interpolated for each temperature, from which the value of the K

_{T}coefficient and the value of the mean grain size for the soaking time t = 0 s were determined (D

_{0}). The values of K

_{T}and D

_{0}are given in Table 4.

_{T}). Figure 4 shows the natural logarithm of the slopes (K

_{T}) of the four lines from Figure 3 plotted as functions of the reciprocal of the absolute temperature (1/T) [18,22].

_{0}according to Equation (8).

^{−1}and proportionality constant K

_{0}= 2.81 × 10

^{−2}mm

^{2}·s

^{−1}.

#### 2.3. Preparation of Welded and Simulated Samples for Comparision Purposes

_{0}and the grain growth activation energy Q, the calculated values of the grain size were compared with the real values. Real grain size values were determined from the welded joint and from the sample simulated on the Gleeble 3500 device (Dynamic Systems, Poestenkill, NY, USA).

_{max}= 1104 °C. The heating rate was determined to be 205 °C·s

^{−1,}and the cooling time t

_{8/5}was 17.5 s (Figure 6). The mean grain size for a given area was determined using the linear intercept method, using the microstructure image obtained by light optical microscopy (LOM) from the center of the sample thickness using ZEISS LSM 700 device (Carl Zeiss AG, Oberkochen, Germany).

_{max}= 1105 °C and the heating rate was determined to be 210 °C·s

^{−1}and time t

_{8/5}was set at 17 s based on Figure 8. The mean grain size for a given area was also determined using the linear intercept method using a microstructure image obtained from the center of the sample by LOM using ZEISS LSM 700 device.

## 3. Results and Discussion

_{calc.}= 22.0 µm.

_{weld.}= 20.6 µm. Based on the comparison, a 6% difference between the estimated and real grain size in the HAZ can be observed.

_{sim.}= 19.4 µm. The difference between the calculated value of the grain size and the grain size of the simulated sample is 12%.

_{0}cannot be replaced by constants obtained from other materials. The reason is the significant difference between these values, which would be the cause of obtaining inaccurate results for austenitic grain size prediction in the HAZ. For example, the values of the activation energy required for grain growth Q obtained by similar experiments can range from 107 to 494 kJ.mol

^{−1}, depending on the material. Additionally, the value of the proportional constant K

_{0}can range from 10

^{−5}to 10

^{1}mm

^{2}·s

^{−1}[11,19,28,29,30]. The reason for such significant differences is the influence of several factors, such as the chemical composition or the presence and size of precipitates, which significantly affect the grain-growth kinetics.

## 4. Summary

^{−1}and proportionality constant K

_{0}= 2.81 × 10

^{−2}mm

^{2}·s

^{−1}. To verify the results, the values of calculated mean grain size were compared to real mean grain size values obtained from the welded joint and physical simulation. The comparisons showed that the values of the grain sizes measured in the HAZ of the welded joint and in the simulated sample reached values that differed from 6% to 12% compared to the values determined by the calculation for the given temperature.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Burke, J.E.; Turnbull, D. Recrystallization and grain growth. Prog. Met. Phys.
**1952**, 3, 220–244. [Google Scholar] [CrossRef] - Webel, J.; Herges, A.; Britz, D.; Detemple, E.; Flaxa, V.; Mohrbacher, H.; Mücklich, F. Tracing Microalloy Precipitation in Nb-Ti HSLA Steel during Austenite Conditioning. Metals
**2020**, 10, 243. [Google Scholar] [CrossRef][Green Version] - Endo, S.; Nakata, N. Development of Thermo-Mechanical Control Process (TMCP) and High Performance Steel in JFE Steel. JFE Tech. Rep.
**2015**, 20, 1–7. [Google Scholar] - Funakawa, Y.; Shiozaki, T.; Tomita, K.; Yamamoto, T.; Maeda, E. Development of High Strength Hot-rolled Sheet Steel Consisting of Ferrite and Nanometer-sized Carbides. ISIJ Int.
**2004**, 44, 1945–1951. [Google Scholar] [CrossRef] - Mičian, M.; Frátrik, M.; Kajánek, D. Influence of Welding Parameters and Filler Material on the Mechanical Properties of HSLA Steel S960MC Welded Joints. Metals
**2021**, 11, 305. [Google Scholar] [CrossRef] - Hochhauser, F.; Ernst, W.; Rauch, R.; Vallant, R.; Enzinger, N. Influence of the Soft Zone on the Strength of Welded modern HSLA Steels. Weld. World
**2012**, 56, 77–85. [Google Scholar] [CrossRef] - Schneider, C.; Ernst, W.; Schnitzer, R.; Staufer, H.; Vallant, R.; Enzinger, N. Welding of S960MC with undermatching filler material. Weld. World
**2018**, 62, 801–809. [Google Scholar] [CrossRef][Green Version] - Amraei, M.; Ahola, A.; Afkhami, S.; Björk, T.; Heidarpour, A. Effects of heat input on the mechanical properties of butt-welded high and ultra-high strength steels. Eng. Struct.
**2019**, 198, 109460. [Google Scholar] [CrossRef] - Rahman, M.; Albu, M.; Enzinger, N. On the modelling of austenite grain growth in micro-alloyed HS steel S700MC. Math. Model. Weld Phenom.
**2012**, 10, 623–636. [Google Scholar] - Lee, S.-J.; Lee, Y.-K. Effect of Austenite Grain Size on Martensitic Transformation of a Low Alloy Steel. Mater. Sci. Forum
**2005**, 475–479, 3169–3172. [Google Scholar] [CrossRef] - Banerjee, K.; Militzer, M.; Perez, M.; Wang, X. Nonisothermal Austenite Grain Growth Kinetics in a Microalloyed X80 Linepipe Steel. Metall. Mater. Trans. A
**2010**, 41A, 3161–3172. [Google Scholar] [CrossRef] - Chen, R.C.; Hong, C.; Li, J.J.; Zheng, Z.Z.; Li, P.C. Austenite grain growth and grain size distribution in isothermal heat.treatment of 300M steel. Procedia Eng.
**2017**, 207, 663–668. [Google Scholar] [CrossRef] - Yu, H.; Wu, K.; Dong, B.; Liu, J.; Liu, Z.; Xiao, D.; Jin, X.; Liu, H.; Tai, M. Effect of Heat-Input on Microstructure and Toughness of CGHAZ in a High-Nb-Content Microalloyed HSLA Steel. Materials
**2022**, 15, 3588. [Google Scholar] [CrossRef] [PubMed] - Shi, M.; Zhang, P.; Wang, C.; Zhu, F. Effect of High Heat Input on Toughness and Microstructure of Coarse Grain Heat Affected Zone in Zr Bearing Low Carbon Steel. ISIJ Int.
**2014**, 54, 932–937. [Google Scholar] [CrossRef][Green Version] - Taillard, R.; Verrier, P.; Maurickx, T.; Foct, J. Effect of Silicon on CGHAZ Toughness and Microstructure of Microalloyed Steels. Metall. Mater. Trans. A
**1995**, 26A, 447–457. [Google Scholar] [CrossRef] - Mičian, M.; Harmaniak, D.; Nový, F.; Winczek, J.; Moravec, J.; Trško, L. Effect of the t8/5 Cooling Time on the Properties of S960MC Steel in the HAZ of Welded Joints Evaluated by Thermal Physical Simulation. Metals
**2020**, 10, 229. [Google Scholar] [CrossRef][Green Version] - Giumelli, A. Austenite Grain Growth Kinetics and the Grain Size Distribution. Ph.D. Thesis, The University of British Columbia, Vancouver, BC, Canada, 6 April 1995. [Google Scholar]
- Abbaschian, R.; Abbaschian, L.; Reed-Hill, R.E. Physical Metallurgy Principles, 4th ed.; Cengage Learning: Stamford, CT, USA, 2009; pp. 244–249. [Google Scholar]
- Moravec, J.; Nováková, I.; Sobotka, J.; Neuman, H. Determination of Grain Growth Kinetics and Assessment of Welding Effect on Properties of S700 MC Steel in the HAZ of Welded Joints. Metals
**2019**, 9, 707. [Google Scholar] [CrossRef][Green Version] - Manohar, P.A.; Dunne, D.P.; Chandra, T.; Killmore, C.R. Grain Growth Predictions in Microalloyed Steels. ISIJ Int.
**1996**, 36, 194–200. [Google Scholar] [CrossRef][Green Version] - Cahn, R.W.; Haasen, P. Physical Metallurgy, Volume 3, 4th ed.; Elsevier Science Ltd.: Amsterdam, The Netherlands, 1996; p. 2475. [Google Scholar]
- Najafkhani, F.; Kheiri, S.; Pourbahari, B.; Mirzadeh, H. Recent advances in the kinetics of normal/abnormal grain growth: A review. Arch. Civ. Mech. Eng.
**2021**, 21, 29. [Google Scholar] [CrossRef] - Bhattacharyya, J.J.; Agnew, S.R.; Muralidharan, G. Texture enhancement during grain growth of magnesium alloy AZ31B. Acta Mater.
**2015**, 86, 80–94. [Google Scholar] [CrossRef][Green Version] - Sellars, C.M.; Whiteman, J.A. Recrystallization and grain growth in hot rolling. Metal. Sci.
**1979**, 13, 187–194. [Google Scholar] [CrossRef] - Maalekian, M.; Radis, R.; Militzer, M.; Moreau, A.; Poole, W.J. In situ measurement and modelling of austenite grain growth in a Ti/Nb microalloyed steel. Acta Mater.
**2012**, 60, 1015–1026. [Google Scholar] [CrossRef] - Strenx. Welding of Strenx; SSAB AB: Stockholm, Sweden, 2017. [Google Scholar]
- Nowotnik, A.; Siwecki, T. The effect of TMCP parameters on the microstructure and mechanical properties of Ti-Nb microalloyed steel. J. Microsc.
**2009**, 237, 258–262. [Google Scholar] [CrossRef] - Moravec, J. Determination of the Grain Growth Kinetics as a Base Parameter for Numerical Simulations demand. MM Sci. J.
**2015**, 10, 649–653. [Google Scholar] [CrossRef] - Seikh, A.H.; Soliman, M.S.; AlMajid, A.; Alhajeri, K.; Alshalfan, W. Austenite Grain Growth Kinetics in API X65 and X70 Steel During Isothermal Heating. Adv. Mater. Sci. Eng.
**2014**, 5, 1–8. [Google Scholar] [CrossRef][Green Version] - Pous-Romero, H.; Lonardelli, I.; Cogswell, D.; Bhadeshia, H.K.D.H. Austenite grain growth in a nuclear pressure vessel steel. Mater. Sci. Eng. A
**2013**, 567, 72–79. [Google Scholar] [CrossRef]

**Figure 2.**EBSD analysis of samples heated to (

**a**) 900 °C, (

**b**) 1000 °C, (

**c**) 1100 °C, and (

**d**) 1200 °C, with soaking time 1 h (IPF X—left, band contrast—right).

**Figure 6.**Thermal cycle of assessed welded joint [5].

**Figure 10.**Microstructure of the sample simulated on Gleeble 3500 device exposed to temperature 1100 °C.

R_{p0.2}(MPa) | R_{m}(MPa) | A_{50mm}(%) | CET (CEV) | KV −20 °C (J) |
---|---|---|---|---|

1018 | 1108 | 10 | 0.26 (0.50) | 32 |

C | Si | Mn | P | S | Al | Nb | V |

0.085 | 0.18 | 1.06 | 0.01 | 0.003 | 0.036 | 0.002 | 0.007 |

Ti | Cu | Cr | Ni | Mo | N | B | Fe |

0.026 | 0.01 | 1.08 | 0.07 | 0.109 | 0.005 | 0.0015 | bal. |

S960MC | Soaking Time (h) | |||||
---|---|---|---|---|---|---|

0.5 | 1 | 2 | 4 | 6 | 8 | |

900 °C | 13.1 | 15.4 | 16.0 | 16.8 | 20.4 | 24.7 |

1000 °C | 25.3 | 26.0 | 29.4 | 30.8 | 32.8 | 39.2 |

1100 °C | 38.5 | 39.2 | 45.5 | 48.8 | 54.1 | 58.8 |

1200 °C | 60.1 | 64.5 | 71.4 | 80.0 | 95.2 | 111.1 |

**Table 4.**Values of initial grain size D

_{0}and partial exponential constants K

_{T}for a given temperature.

S960MC | K_{T} (mm^{2}s^{−1}) | D_{0} (mm) |
---|---|---|

900 °C | 1.426 × 10^{−8} | 0.0120 |

1000 °C | 2.965 × 10^{−8} | 0.0240 |

1100 °C | 7.248 × 10^{−8} | 0.0371 |

1200 °C | 3.063 × 10^{−7} | 0.0532 |

**Table 5.**Welding parameters of welded joint [5].

Method | U (V) | I (A) | Welding Speed (cm·min^{−1}) | Wire Feed Speed v_{d}(m·min ^{−1}) | Heat Input Q_{p} (kJ·cm^{−1}) | Weld Gap b (mm) |
---|---|---|---|---|---|---|

GMAW-S | 16.6 | 102 | 22.2 | 3.8 | 3.69 | 1.5 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mičian, M.; Frátrik, M.; Moravec, J.; Švec, M. Determination of Grain Growth Kinetics of S960MC Steel. *Materials* **2022**, *15*, 8539.
https://doi.org/10.3390/ma15238539

**AMA Style**

Mičian M, Frátrik M, Moravec J, Švec M. Determination of Grain Growth Kinetics of S960MC Steel. *Materials*. 2022; 15(23):8539.
https://doi.org/10.3390/ma15238539

**Chicago/Turabian Style**

Mičian, Miloš, Martin Frátrik, Jaromír Moravec, and Martin Švec. 2022. "Determination of Grain Growth Kinetics of S960MC Steel" *Materials* 15, no. 23: 8539.
https://doi.org/10.3390/ma15238539