# Kinetic Model of Isothermal Bainitic Transformation of Low Carbon Steels under Ausforming Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}concept as a thermodynamic limit of CFB transformation to design advanced carbon CFB steels with an ultra-fine structure (RA thickness < 100 nm). They achieved prominent steel properties, including strength and elongation of about 2.2–2.5 GPa and 20–30%, respectively. However, the concept is successful only in high- and medium-carbon steels (0.4–1.0 wt.%C), whereby transformation at very low temperatures above the martensite start temperature is necessary. Despite the attempt to take low-carbon steels (<0.2% C) into account, higher Gibbs free energy, associated with the insufficient C enrichment in austenite affected by the lower bulk density of C, has promoted the thermal instability of the austenite during the cooling process after isothermal holding.

_{0}concept and the empirical Koistinen–Marburger (KM) equation. The activation energy, nucleation activity, and carbon enrichment variations caused by the process contributions are also correlated with the kinetics of isothermal bainitic transformation. By means of the model, the thermal stability of austenite can be appropriately adjusted with an optimal design of the processing parameters of the ausforming and alloy modification of low-carbon CFB steels.

## 2. Materials and Methods

#### 2.1. As-Received Materials

#### 2.2. Experiment

^{−1}, and cooled to the isothermal temperature within the same period, as was conducted for the PIT samples. To examine changes in the martensite start (${M}_{\mathrm{s}}$) temperature, a specimen of each material was directly quenched from the austenitizing temperature. It was defined as the DQ specimen, and the volumetric expansion result was set as a reference. The ${M}_{\mathrm{s}}$ locus of the DQ specimens was captured from the first deviation of the dilation curve during cooling, whereas that of the AIT specimens was traced in the same manner specifically during the secondary stage of cooling after isothermal tempering. In the case of the DQ specimens, the volumetric transformations of the martensite were calculated by using a total volumetric expansion with respect to the relative tangent of the dilatation curve as a reference, bearing in mind that in this research the ${M}_{\mathrm{s}}$ temperature was also empirically estimated, using the following equation [30,31].

#### 2.3. Characterization

## 3. Transformation Models

#### 3.1. Transformation Models

#### 3.1.1. Nucleation Rate Model

#### 3.1.2. Activation Energy

^{−10}m for the FCC planes [44].

#### 3.1.3. Potential Nucleation Site Density

^{−1}and depend slightly on the chemical composition [21,43]. A fundamental difference between the nucleation of martensite and bainite is that the density of the pre-existing defects for martensite nucleation is governed by the prior austenitic grain size, whereas the bainitic nucleation is also controlled by the structural interfaces, namely the $\mathsf{\gamma}/\mathsf{\gamma}$ and $\mathsf{\gamma}/\mathsf{\alpha}$ interfaces. According to Van Bohemann and Seitma’s report [22], $m$ can be replaced by ${b}_{\mathrm{GB}}$ and ${b}_{\mathrm{AN}}$ with consideration of the effects of the $\mathsf{\gamma}/\mathsf{\gamma}$ and $\mathsf{\gamma}/\mathsf{\alpha}$ interfaces, respectively. The density of the available $\mathsf{\gamma}/\mathsf{\gamma}$ interfaces is dependent on the volume fraction of the remaining available austenite and the austenite grain size. The ${b}_{\mathrm{GB}}$ parameter is thus given as follows.

#### 3.1.4. Austenitic Phase Fraction as a Function of Carbon Enrichment

#### 3.1.5. Bainitic Transformation Model

^{3}. Consequently, the kinetics of the isothermal bainitic transformation can be calculated by means of a numerical integration of the associated nucleation rates. The product of the integration is given by the following equation.

#### 3.2. Martensitic Transformation

## 4. Results and Discussion

#### 4.1. Experimentally Determined Phase Fractions

#### 4.2. Modelling Results

#### 4.2.1. M_{s} Temperature

#### 4.2.2. Model Parameters

#### 4.2.3. Kinetics of Bainitic Phase Transformation

#### 4.2.4. Dislocation Density Estimation

## 5. Conclusions/Summary

- The formation of bainitic ferrite is mainly governed by two factors: carbon enrichment in austenite and the activation energy as an energy barrier required for nucleation.
- Ausforming accelerates the onset of the bainitic phase transformation but results in sluggish transformation due to the mechanical stabilization of austenite. A higher degree of ausforming is more applicable in the steel with lower carbon content. With the substantial development of nucleation sites, even though they provide a slightly lower fraction of bainitic ferrite, the result effectively resists the formation of fresh martensite by improving the thermal stability of austenite.
- A fitting parameter representing the initial energy barrier can be used to examine the activation energy change caused by ausforming. A decrease in the energy barrier allows the acceleration of the transformation. While the transformation progresses, the driving energy for autocatalytic nucleation becomes smaller due to the enhancement of the dislocation density.
- The impact of carbon content plays a slight role in the onset period, but it is more pronounced during the progress of bainitic transformation. Minimizing carbon concentration in steel gives rise to a decrease in the net activation energy difference with the increasing of the nucleation rate. The result allocates a higher density of nucleation sites with more bainitic ferrite fractions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Graphical illustrations of the isothermal decomposition of austenite into bainite for PIT and AIT specimens, and (

**b**) schematic diagram showing relationships of Gibbs free energy, temperature, and composition of steels under various heat treatments. NS, GB, UA, BF, and FM stand for nucleation site, grain boundary, untransformed austenite, bainitic ferrite, and fresh martensite, respectively.

**Figure 2.**(

**a**) Phase quantifications of examined steels using XRD measurement and (

**b**) volumetric strain of DQ and AIT specimens after cooling from austenitizing and deformation stage.

**Figure 4.**The kinetics of bainitic transformation of (

**a**) MC1.5Mn1NiCr and (

**b**) LC2.5Mn0.2NiCr steels under PIT and AIT with the strain of 0.15 and 0.35.

**Figure 5.**Relationship between the austenite decomposition and the degree of carbon enrichment in austenite of MC1.5Mn1NiCr steel with PIT condition.

**Figure 6.**Nucleation rate as a function of BF volume fraction for (

**a**) MC1.5Mn1NiCr and (

**b**) LC2.5Mn0.2NiCr steels under various conditions.

**Figure 7.**Driving force for autocatalytic nucleation as a function of density of nucleation sites of (

**a**) MC1.5Mn1NiCr and (

**b**) LC2.5Mn0.2NiCr steels under various conditions.

**Figure 8.**Variation of total activation energy difference with bainite formation evolution of (

**a**) MC1.5Mn1NiCr and (

**b**) LC2.5Mn0.2NiCr steels under various conditions.

**Figure 9.**(

**a**) Dislocation density estimation and (

**b**) prior austenite grain size of MC1.5Mn1NiCr and LC2.5Mn0.2NiCr steels under PIT, AIT0.15, and AIT0.35 treatments.

Steel | Fe | C | Si | Mn | Cr | Ni | B | Ti |
---|---|---|---|---|---|---|---|---|

MC1.5Mn1NiCr | Bal. | 0.26 | 1.07 | 1.46 | 0.99 | 0.98 | 0.0031 | 0.027 |

LC2.5Mn0.2NiCr | Bal. | 0.18 | 0.97 | 2.50 | 0.20 | 0.21 | 0.0018 | 0.033 |

**Table 2.**Volume phase fraction determined by means of quantitative analysis of XRD measurement combined with the dilatometry results.

Material/Condition | Volume Fraction, % | ${\mathit{w}}_{\mathbf{\gamma}\mathbf{,}\mathbf{RA}}\mathbf{\left(}\mathbf{=}{\mathit{x}}_{\mathbf{C}}\mathbf{\right)}$ Equation (3) | ||
---|---|---|---|---|

RA | BF | FM | ||

MC1.5Mn1NiCr/DQ | - | - | 100 | - |

MC1.5Mn1NiCr/PIT | 15.6 ± 3.3 | 77.4 ± 4.2 | 7.0 ± 2.8 | 0.78 |

MC1.5Mn1NiCr/AIT0.15 | 14.6 ± 5.1 | 62.0 ± 6.7 | 23.4 ± 6.3 | 0.68 |

MC1.5Mn1NiCr/AIT0.35 | 13.5 ± 5.8 | 47.9 ± 4.5 | 38.6 ± 3.4 | 0.56 |

LC2.5Mn0.2NiCr/DQ | 1.2 ± 0.8 | - | 98.5 ± 2.8 | 0.04 |

LC2.5Mn0.2NiCr/PIT | 8.5 ± 2.5 | 83.6 ± 4.6 | 7.9 ± 3.9 | 0.45 |

LC2.5Mn0.2NiCr/AIT0.15 | 11.3 ± 3.7 | 77.6 ± 3.4 | 11.1 ± 4.5 | 0.51 |

LC2.5Mn0.2NiCr/AIT0.35 | 16.9 ± 3.5 | 74.3 ± 4.9 | 8.8 ± 4.1 | 0.89 |

**Table 3.**Determined kinetics parameters using the modified KM equation for the examined MC1.5Mn1NiCr and LC2.5Mn0.2NiCr steels under PIT and AIT conditions.

Material/Condition | ${\mathit{\alpha}}_{\mathbf{FM}},{\mathit{K}}^{-1}$ | $\mathit{n}\mathbf{,}\mathbf{-}$ | ${\mathit{M}}_{\mathbf{s}\mathbf{,}\mathbf{exp}}\mathbf{,}\mathbf{C}$ | ${\mathit{M}}_{\mathbf{s}\mathbf{,}\mathbf{cal}}\mathbf{,}\mathbf{C}$ |
---|---|---|---|---|

MC1.5Mn1NiCr/DQ | 0.0205 | 0.96 | 354 ± 5.1 | 344 |

MC1.5Mn1NiCr/PIT | 0.0205 | 0.96 | 347 ± 4.7 | 332 |

MC1.5Mn1NiCr/AIT0.15 | 0.0205 | 0.96 | 260 ± 7.1 | 255 |

MC1.5Mn1NiCr/AIT0.35 | 0.0205 | 0.96 | 265 ± 6.3 | 260 |

LC2.5Mn0.2NiCr/DQ | 0.0243 | 1.06 | 388 ± 2.4 | 380 |

LC2.5Mn0.2NiCr/PIT | 0.0243 | 1.06 | 351 ± 4.2 | 345 |

LC2.5Mn0.2NiCr/AIT0.15 | 0.0243 | 1.06 | 270 ± 3.6 | 263 |

LC2.5Mn0.2NiCr/AIT0.35 | 0.0243 | 1.06 | 192 ± 5.8 | 184 |

Parameter | MC1.5Mn1NiCr | LC2.5Mn0.2NiCr | ||||
---|---|---|---|---|---|---|

PIT | AIT0.15 | AIT0.35 | PIT | AIT0.15 | AIT0.35 | |

${d}_{\mathsf{\gamma}},\mathsf{\mu}\mathrm{m}$ | 48 ± 1.5 | 43 ± 3.3 | 35 ± 2.1 | 56 ± 0.9 | 49 ± 1.4 | 44 ± 2.2 |

${T}_{\mathrm{iso}},K$ | 673 | 673 | ||||

${T}_{\mathrm{h}\overline{\mathrm{X}}},K$ | 753 | 983 | ||||

${C}_{1}$ | 2304 | 2205 | ||||

${T}_{0\overline{\mathrm{X}}}^{\prime},K$ | 763 | 778 | ||||

${C}_{2}$ | 8911 | 8537 |

Parameter | MC1.5Mn1NiCr | LC2.5Mn0.2NiCr | ||||
---|---|---|---|---|---|---|

PIT | AIT0.15 | AIT0.35 | PIT | AIT0.15 | AIT0.35 | |

${w}_{\mathsf{\alpha}}$, mole fraction | 0.0091 | 0.0056 | 0.00081 | 0.0060 | 0.0048 | 0.0031 |

${Q}_{0}^{*}$, kJ/mole | 172.98 | 166.48 | 170.9 | 167.53 | 164.83 | 145.74 |

${d}_{\mathrm{s}}$ | 1.47 | 19.26 | 12.03 | 1.81 | 4.36 | 9.73 |

${K}_{1}$ | 0.46 | 4.86 | 7.32 | 0.36 | 0.69 | 1.29 |

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**MDPI and ACS Style**

Kumnorkaew, T.; Lian, J.; Uthaisangsuk, V.; Bleck, W.
Kinetic Model of Isothermal Bainitic Transformation of Low Carbon Steels under Ausforming Conditions. *Alloys* **2022**, *1*, 93-115.
https://doi.org/10.3390/alloys1010007

**AMA Style**

Kumnorkaew T, Lian J, Uthaisangsuk V, Bleck W.
Kinetic Model of Isothermal Bainitic Transformation of Low Carbon Steels under Ausforming Conditions. *Alloys*. 2022; 1(1):93-115.
https://doi.org/10.3390/alloys1010007

**Chicago/Turabian Style**

Kumnorkaew, Theerawat, Junhe Lian, Vitoon Uthaisangsuk, and Wolfgang Bleck.
2022. "Kinetic Model of Isothermal Bainitic Transformation of Low Carbon Steels under Ausforming Conditions" *Alloys* 1, no. 1: 93-115.
https://doi.org/10.3390/alloys1010007