# Dynamic Recrystallization Kinetics of As-Cast Fe-Cr-Al-La Stainless Steel during Hot Deformation

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}. The true stress-true strain curves were obtained and their characteristics were analyzed. Using regression analysis, the apparent activation energy for the Fe-20Cr-5.5Al-0.64La stainless steel was estimated to be 300.19 kJ/mol, and the constitutive equation was developed successfully with a hyperbolic sine equation as: $\dot{\epsilon}={e}^{21.91}{\left[\mathrm{sinh}\left(0.035\sigma \right)\right]}^{3.18}\mathrm{exp}\left(\frac{-300190}{RT}\right)$. The critical strain, the peak strain and the strain for the maximum softening rate were identified based on the work hardening rate curves and expressed as a function of the Zener−Hollomon parameter. The kinetic model of DRX was established using the stress−strain data. According to the analysis of the kinetics model and microstructure evolution, the evolution of DRX volume could be described as follows: the volume fraction of DRX grains increased with an increase in strain; at a fixed deformation temperature, the DRX volume fraction was larger at a lower strain rate for the same strain; and the size of DRX grains increased with an increase in temperature or a decrease in strain rate.

## 1. Introduction

## 2. Materials and Methods

^{−1}. The cylindrical specimens were compressed axially. Temperature changes during the hot compression were monitored by a thermocouple that was welded at the mid-height of the specimens. During the tests, the specimens were first heated to 1250 °C at a rate of 5 K/s and held for 3 min to ensure homogenization. Then, they were cooled to the predetermined temperatures at a cooling speed of 10 K/s. After isothermal holding for 60 s, the specimens were hot compressed to a height reduction of 20%, 40% and 60% (true strain of 0.223, 0.511 and 0.916), respectively. All specimens were quenched in water immediately after deformation to retain their microstructure. All tests were carried out in an argon atmosphere to prevent oxidation of the samples. The variation of true stress ($\sigma $) with true strain ($\epsilon $) was recorded automatically per half a second by a computer at each deformation condition during isothermal compression. After the tests, the specimens were cut symmetrically along the axis. On the cut surface, the microstructure was observed with optical microscopy after conventional polishing and etching with a chloride solution (20 g FeCl

_{3}+ 30 mL HCl + 100 mL distilled water).

## 3. Results and Discussion

#### 3.1. Flow Curves

^{−1}, a peak appears on each flow curve, followed by a lower flow stress, which is thought to be characteristic of the occurrence of dynamic recrystallization [26,27]. When the strain rate is less than 0.01 s

^{−1}, the stress declines slightly after the peak points of the flow curves, which is very similar to the studies of DRX in some ferritic alloys [20,28,29]. Work hardening generally results from dislocation rising quickly as strain increases. Dynamic softening, such as DRX, may occur when strain reaches a certain level, partially offsetting the work hardening effect [26]. With an increase in strain rate and a decrease in deformation temperature, the Fe-Cr-Al-La stainless steel shows sensitivity to the changes in strain rate and deformation temperature, and the peak stress and steady flow stress increase. This inhibits DRX from taking place, and as a result, the deformed specimens exhibit more work hardening. The reason is that a higher strain rate and a lower deformation temperature will shorten the energy accumulation time and reduce the boundary mobility, leading to the hindrance of nucleation and growth of dynamic recrystallized grains and the disappearance of dislocation [30,31,32,33]. When the strain rate reaches 1 s

^{−1}, the flow curves do not show softening at 1000, 1050, and 1100 °C.

#### 3.2. Determination of DRX Characteristic Parameters

^{−1}and at 1150 °C is shown in Figure 3. Kim et al. [35,36] found that the critical stress (${\sigma}_{c}$) and the peak stress (${\sigma}_{p}$) divide the $\theta -\sigma $ curve into three segments. The rate of work hardening is positive in the first and second segments. In the first segment, the curve has a greater slope and decreases rapidly. When ${\partial}^{2}\theta /\partial {\sigma}^{2}=0$, dynamic recrystallization begins to occur, and the corresponding strain is the critical strain (${\epsilon}_{c}$) of DRX. As the strain continues to increase, $\theta $ decreases slowly in the second segment because the work hardening is partially offset by DRX. The values of ${\sigma}_{p}$ and the peak strain (${\epsilon}_{p}$) can be determined at the first emergence of $\theta =0$ [37]. In the third segment, from the peak stress to the steady state stress (σ

_{ss}), the work hardening rate changes to negative, which means that the dynamic softening caused by DRX is more effective than the work hardening. The strain and stress for the maximum softening rate (${\epsilon}^{*}$ and ${\sigma}^{*}$) are determined when $\theta $ decreases to the valley point in the $\theta -\sigma $ curve [38]. When $\theta $ again equals to zero, DRX develops completely, and DRX softening and work hardening are balanced.

#### 3.3. Constitutive Equations

^{−1}), $Q$ is the apparent activation energy for hot deformation (J/mol), R is the universal gas constant (8.314 J mol

^{−1}K

^{−1}), T is the deformation temperature (K), A and $\alpha $ are the material constants, and n is the stress exponent. The value of Q, which is influenced by the material’s chemical compositions and as-received status, indicates the deformation difficulty of the alloy [43].

_{1}, MPa

^{−1}.

^{−1}). Some scholars [16] have shown that $\sigma $ can be represented by the peak stress (${\sigma}_{p}$) for DRX in metals. The plots of $\mathrm{ln}\dot{\epsilon}-\mathrm{ln}{\sigma}_{p}$, $\mathrm{ln}\dot{\epsilon}-{\sigma}_{p}$, and $\mathrm{ln}\dot{\epsilon}-\mathrm{ln}\mathrm{sinh}\left(\alpha {\sigma}_{p}\right)$ at different temperatures, as shown in Figure 5, can be obtained by submitting the peak stress to Equations (4)–(6). The mean values of all slope rates in Figure 5a and b are accepted as the material constants ${n}_{1}$ and $\beta $, thus ${n}_{1}=4.26$, $\beta =0.15$ MPa

^{−1}, and $\alpha =\beta /{n}_{1}=0.035$ MPa

^{−1}. In Figure 5c, the slopes of the straight lines obtained by linear regression at different temperatures are similar, which proves that Equation (1) can correctly describe the flow curves in Figure 2. The average value of ${n}_{2}$ at different temperatures is then calculated as 3.17.

_{p}and the Z parameter can be calculated from Equation (10):

#### 3.4. DRX Kinetic Model

^{−1}is shown in Figure 9. According to the linear fitting relation, m and k are calculated to be 4.958 and 2.534, respectively. Therefore, the DRX kinetic model at 1150 °C and 1 s

^{−1}can be expressed by the following equation:

_{DRX}is larger at a lower strain rate for the same strain. This is because the grain boundary mobility increases with a decrease in strain rate, which accelerates the dynamic recrystallization.

#### 3.5. Microstructure Evolution and DRX Mechanism

^{−1}according to various strains. It can be seen from Figure 11a that the original grains in the as-cast steel are very coarse. As shown in Figure 11b, serrated grain boundaries appeared when the strain is 0.223. Some fine grains are formed at the original grain boundaries and the triple junction. This means that DRX occurs under this condition [47]. The banded dislocation substructures appear inside the original grains, as indicated by the blue arrows. Figure 11c shows that more and more fine DRX grains are formed at the original grain boundaries and inside the coarse grains at a strain of 0.511. When strain increases to 0.916, dynamic recrystallization is fully developed, and the volume fraction of DRX grains (${X}_{\mathrm{DRX}}$) reaches one, as shown in Figure 11d. The above analysis shows that ${X}_{\mathrm{DRX}}$ increases with an increase in strain, which is in good agreement with the DRX kinetic models.

^{−1}, are shown in Figure 12. The original coarse grain boundaries and DRX grains can be clearly distinguished. The dynamic recrystallization volume fraction increases with a decrease in strain rate under the given temperature and strain conditions. Figure 12a,b also prove that fine recrystallized grains initially form at the original grain boundaries.

^{−1}and different temperatures. It can be seen from Figure 12 and Figure 13 that the size of dynamic recrystallization grains increases with an increase in temperature or a decrease in strain rate. This is because a higher temperature results in a higher grain boundary migration ability and a lower strain rate gives the recrystallization nucleus more time to grow [48,49].

## 4. Conclusions

^{−1}. The following conclusions are drawn:

- The flow stress of the Fe-Cr-Al-La stainless steel increases with a decrease in deformation temperature and an increase in strain rate. Most of the flow curves exhibit a single peak, followed by a steady-state flow, which is a typical DRX softening characteristic. The low deformation temperature and high strain rate prevent the evolution of DRX.
- The apparent activation energy in the test conditions for the Fe-20Cr-5.5Al-0.64La stainless steel was calculated to be 300.19 kJ/mol. The constitutive equation was established with a hyperbolic sine equation by regression analysis and can be identified as: $\dot{\epsilon}={e}^{21.91}{\left[\mathrm{sinh}\left(0.035\sigma \right)\right]}^{3.18}\mathrm{exp}\left(\frac{-300190}{RT}\right)$ or expressed as a function of the Z parameter: $\sigma =\frac{1}{0.035}\mathrm{ln}\left\{{\left(\frac{Z}{3.28\times {10}^{9}}\right)}^{\frac{1}{3.18}}+{\left[{\left(\frac{Z}{3.28\times {10}^{9}}\right)}^{\frac{2}{3.18}}+1\right]}^{\frac{1}{2}}\right\}$. The correlations between the critical strain, the peak strain and the strain for maximum softening rate with the Z parameter were also obtained.
- Kinetics model of DRX was established to predict the microstructure evolution. The dynamic recrystallization kinetics at 1150 °C and 1 s
^{−1}can be expressed as: $\left(\right)open="\{">\begin{array}{c}{X}_{\mathrm{DRX}}=0\left(\epsilon {\epsilon}_{c}\right)\\ {X}_{\mathrm{DRX}}=1-\mathrm{exp}\left[-2.534{\left(\frac{\epsilon -0.074}{0.324}\right)}^{4.958}\right]\left(\epsilon \ge {\epsilon}_{c}\right)\end{array}$ - Both the dynamic recrystallization kinetic model and microstructure observation show that the DRX volume fraction is larger at a lower strain rate for the same strain when the deformation temperature is fixed.
- The microstructure observation shows that fine DRX grains initially form at the original grain boundaries. The volume fraction of DRX grains increases with an increase in strain. The microstructure observation also validated the dynamic recrystallization kinetic model. The size of dynamic recrystallization grains increases with an increase in temperature or a decrease in strain rate.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**True stress−strain curves of the specimens which height reduction is 60% under different deformation conditions: (

**a**) 1000 °C; (

**b**) 1050 °C; (

**c**) 1100 °C; and (

**d**) 1150 °C.

**Figure 4.**θ vs. $\sigma $ plots for Fe-Cr-Al-La stainless steel at strain rates of (

**a**) 0.1 s

^{−1}, (

**b**) 0.01 s

^{−1}and (

**c**) 0.001 s

^{−1}.

**Figure 5.**Relationship between peak stress and strain rate of Fe-Cr-Al-La stainless steel: (

**a**) relationship of $\mathrm{ln}\dot{\epsilon}-\mathrm{ln}{\sigma}_{p}$; (

**b**) relationship of $\mathrm{ln}\dot{\epsilon}-{\sigma}_{p}$; and (

**c**) relationship of $\mathrm{ln}\dot{\epsilon}-\mathrm{ln}\mathrm{sinh}\left(\alpha {\sigma}_{p}\right)$.

**Figure 6.**The linear relationship between $\mathrm{ln}\left(\mathrm{sinh}\alpha {\sigma}_{p}\right)$ and 1/T.

**Figure 7.**The relationship between lnZ and $\mathrm{ln}\mathrm{sinh}\left(\alpha {\sigma}_{p}\right)$.

**Figure 9.**The relationship between $\mathrm{ln}\left[-\mathrm{ln}\left(1-{X}_{\mathrm{DRX}}\right)\right]$ and $\mathrm{ln}\left[\frac{\left(\epsilon -{\epsilon}_{c}\right)}{{\epsilon}^{*}}\right]$ at 1150 °C and 1 s

^{−1}.

**Figure 10.**The curves of DRX kinetics under various conditions: (

**a**) 1150 °C, (

**b**) 1100 °C, (

**c**) 1050 °C, and (

**d**) 1000 °C.

**Figure 11.**The DRX evolution of Fe-Cr-Al-La stainless steel at 1000 °C and 0.1 s

^{−1}to various strains: (

**a**) 0, (

**b**) 0.223, (

**c**) 0.511, and (

**d**) 0.916.

**Figure 12.**Deformation microstructure of Fe-Cr-Al-La stainless steel compressed to a strain of 0.223 at 1150 °C and at a strain rate of (

**a**) 1 s

^{−1}, (

**b**) 0.1 s

^{−1}, (

**c**) 0.01 s

^{−1}, and (

**d**) 0.001 s

^{−1}.

**Figure 13.**Deformation microstructure of Fe-Cr-Al-La stainless steel compressed to a strain of 0.916 at a strain rate of 0.1 s

^{−1}and at (

**a**) 1150 °C, (

**b**) 1100 °C, (

**c**) 1050 °C, and (

**d**) 1000 °C.

C | Si | Mn | P | S | Cr | Al | La | Fe + Others |
---|---|---|---|---|---|---|---|---|

0.042 | 0.28 | 0.19 | 0.0076 | 0.0011 | 19.95 | 5.49 | 0.64 | balance |

Temperature (°C) | $\dot{\mathit{\epsilon}}$ (s^{−1})
| ${\mathit{\sigma}}_{\mathit{p}}$ (MPa) | ${\mathit{\epsilon}}_{\mathit{p}}$ | ${\mathit{\sigma}}^{*}$ (MPa) | ${\mathit{\epsilon}}^{*}$ | ${\mathit{\sigma}}_{\mathit{s}\mathit{s}}$ (MPa) | ${\mathit{\epsilon}}_{\mathit{s}\mathit{s}}$ | ${\mathit{\sigma}}_{\mathit{c}}$ (MPa) | ${\mathit{\epsilon}}_{\mathit{c}}$ |
---|---|---|---|---|---|---|---|---|---|

1150 | 1 | 48.25 | 0.177 | 47.3 | 0.324 | 46.49 | 0.471 | 47.55 | 0.074 |

0.1 | 31.34 | 0.165 | 31.11 | 0.232 | 30.52 | 0.461 | 29.75 | 0.070 | |

0.01 | 18.32 | 0.111 | 17.62 | 0.319 | 17.30 | 0.494 | 18.24 | 0.071 | |

0.001 | 11.56 | 0.11 | 11.12 | 0.316 | 10.97 | 0.494 | 11.46 | 0.051 | |

1100 | 0.1 | 38.97 | 0.19 | 38.34 | 0.324 | 37.51 | 0.466 | 36.62 | 0.075 |

0.01 | 24.57 | 0.169 | 23.84 | 0.319 | 23.31 | 0.496 | 24.05 | 0.078 | |

0.001 | 11.91 | 0.097 | 11.76 | 0.277 | 11.54 | 0.44 | 11.86 | 0.066 | |

1050 | 0.1 | 49.86 | 0.185 | 48.78 | 0.317 | 47.87 | 0.444 | 48.95 | 0.074 |

0.01 | 29.67 | 0.168 | 29.27 | 0.264 | 28.6 | 0.438 | 28.97 | 0.086 | |

0.001 | 16.73 | 0.128 | 16.37 | 0.266 | 16.13 | 0.407 | 16.61 | 0.063 | |

1000 | 0.1 | 62.3 | 0.163 | 58.56 | 0.326 | 54.37 | 0.542 | 60.23 | 0.076 |

0.01 | 38.48 | 0.151 | 36.88 | 0.302 | 35.06 | 0.514 | 38.3 | 0.079 | |

0.001 | 20.84 | 0.155 | 20.48 | 0.315 | 20.22 | 0.468 | 20.81 | 0.056 |

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**MDPI and ACS Style**

Deng, Z.; Liu, J.; Shao, J.; McLean, A.
Dynamic Recrystallization Kinetics of As-Cast Fe-Cr-Al-La Stainless Steel during Hot Deformation. *Metals* **2023**, *13*, 692.
https://doi.org/10.3390/met13040692

**AMA Style**

Deng Z, Liu J, Shao J, McLean A.
Dynamic Recrystallization Kinetics of As-Cast Fe-Cr-Al-La Stainless Steel during Hot Deformation. *Metals*. 2023; 13(4):692.
https://doi.org/10.3390/met13040692

**Chicago/Turabian Style**

Deng, Zhenqiang, Jianhua Liu, Jian Shao, and Alexander McLean.
2023. "Dynamic Recrystallization Kinetics of As-Cast Fe-Cr-Al-La Stainless Steel during Hot Deformation" *Metals* 13, no. 4: 692.
https://doi.org/10.3390/met13040692