The Role and Modeling of Ultrafast Heating in Isothermal Austenite Formation Kinetics in Quenching and Partitioning Steel

Abstract

A modified Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, including the heating rates, was proposed in this study to improve the accuracy of isothermal austenite formation kinetics prediction. Since the ultrafast heating process affects the behavior of ferrite recrystallization and austenite formation before the isothermal process, which in turn influences the subsequent isothermal austenite formation kinetics, the effects of varying austenitization temperatures and heating rates on isothermal austenite formation in cold-rolled quenching and partitioning (Q&P) steel, which remain insufficiently understood, were systematically investigated. Under a constant heating rate, the austenite formation rate initially increases and subsequently decreases as the austenitization temperature rises from formation start temperature A_c1 to finish temperature A_c3, and complete austenitization is achieved more quickly at elevated temperatures. At a given austenitization temperature, an increased heating rate was found to accelerate the isothermal transformation kinetics and significantly reduce the duration required to achieve complete austenitization. The experimental results revealed that both the transformation activation energy ($Q$) and material constant ($k_0$) decreased with increasing heating rates, while the Avrami exponent ($n$) showed a progressive increase, leading to the development of the heating-rate-dependent modified JMAK model. The model accurately characterizes the effect of varying heating rates on isothermal austenite formation kinetics, enabling kinetic curves prediction under multiple heating rates and austenitization temperatures and overcoming the limitation of single heating rate prediction in existing models, with significantly broadened applicability.

1. Introduction

The austenite formation constitutes an essential stage in heat treatment processes, where the formation fraction during continuous heating/isothermal holding and the prior austenite grain size (PAGS) critically influence the subsequent martensite transformation during quenching and the carbon partitioning behavior [1,2,3]. These microstructural characteristics ultimately govern the resultant mechanical properties, including strength, hardness, toughness, and ductility [4,5,6]. The quenching and partitioning (Q&P) process has emerged as a prominent technique for developing advanced high-strength steels (AHSS) [7,8,9], owing to its ability to produce an excellent combination of strength and ductility through the transformation-induced plasticity (TRIP) effect of retained austenite during deformation [10,11,12]. The Q&P process involves sequential stages of non-isothermal austenite formation during continuous heating followed by isothermal austenite formation during isothermal holding, subsequent quenching, partitioning, and final quenching to room temperature [2,13]. Consequently, understanding the influence of heating parameters on isothermal austenite formation kinetics is paramount for controlling the austenite fraction during austenitization, which proves crucial for optimizing Q&P processing routes [14] and other AHSS development strategies [15].

The emergence of ultrafast heating techniques has introduced novel approaches for microstructural control during heating in materials processing. In conventional continuous annealing processes characterized by relatively slow heating rates (1–10 °C/s), extensive recrystallization occurs before austenite formation. In contrast, the recently developed induction heating technique, capable of achieving an ultrafast heating rate of up to 1000 °C/s, not only significantly reduces energy consumption and enhances production efficiency, but also simultaneously enables grain refinement with concomitant improvements in both strength and ductility [16,17,18,19].

At present, some researchers have conducted studies on the effects of the ultrafast heating process on non-isothermal austenite formation behavior and model predictions [20,21]. The ultrafast heating process has been observed to significantly delay recrystallization, retaining substantially deformed ferrite, which induces the explosive nucleation of austenite [18]. However, the influence of ultrafast heating on isothermal austenite formation has received little research. The majority of existing studies concerning isothermal austenite transformation have been limited to investigations under slow heating rate conditions [22,23,24,25], with model development concentrating on temperature-dependent formation kinetics. Most researchers have conducted studies on isothermal austenite formation under a single slow condition using the classical Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation [26,27,28,29]. Limited investigations by Ollat et al. [30] and Zheng et al. [31] have partially addressed isothermal transformation kinetics in cold-rolled dual phase (DP) steels at heating rates of 5 °C/s, 30 °C/s, and 50 °C/s. However, formation behavior under higher heating rates conditions remains unexamined. Consequently, certain limitations persist in understanding the effects of the ultrafast heating process on isothermal austenite formation kinetics and corresponding model development.

This study aims to investigate the role of the ultrafast heating process on isothermal austenite formation kinetics and develop a modified JMAK kinetics model including the heating rates variable. The proposed model is devoted to (i) precisely characterizing the isothermal austenite formation behavior, (ii) enabling kinetic curves prediction under multiple heating rates and austenitization temperatures, and (iii) overcoming the limitation of single heating-rate prediction in existing models, with significantly broadened applicability.

2. Experimental Procedures

2.1. Materials

The material used in this study is Q&P steel, with its chemical compositions provided in

Table 1. The chemical compositions of the Q&P 1180 steel (wt.%).

C	Si	Mn	P	S	Cr	Fe
0.19	1.58	1.9	0.0088	0.0014	0.016	Bal.

. The hot rolling process of the steel started at 1220 °C and finished at 855 °C. After pickling the surface oxide scale, the hot-rolled plate was cold rolled with a reduction rate of 65%, achieving a final thickness of 1.6 mm. The rectangular specimens measuring 10 × 4 × 1.6 mm³ were cut from cold-rolled sheets and underwent thermal treatments as follows, with the length direction and rolling direction (RD) of the sheet maintained parallel.

2.2. Thermal Treatments

In order to investigate the effects of the ultrafast heating process on isothermal austenite formation kinetics, thermal dilatometry measurements were conducted using a thermal dilatometer DIL805A/D (BÄHR-Thermoanalyse GmbH, Bahrain, Germany), under various austenitization temperatures and heating conditions.

Firstly, the following thermal treatments were set up to explore the influence of austenitization temperatures (ATs) on the isothermal austenite formation kinetics under different heating rates ($\nu$):

(i) The thermal treatment temperatures of A_c1 + 30/70/110 °C were set under heating rates of 1.78 °C/s, 50 °C/s, and 300 °C/s, as shown in

Table 2. The set values of $\nu$ and AT in the heat treatment.

$\mathit{\nu }$ °C/s	Ac1 °C	Ac3 °C	AT °C
1.78	740	880	770	810	850
50	760	910	790	830	870
300	770	920	800	840	880

. The specimens were heated at a specific heating rate to the designated temperature and held for 200 s to undergo isothermal austenite transformation, followed by reheating to 1100 °C at the same heating rate to achieve full austenitization and obtain a complete thermal expansion curve, thereby calculating the austenite fraction during the isothermal process. Subsequently, the test steels were quenched to room temperature at a cooling rate of 100 °C/s.

(ii) Furthermore, microstructural characterization was performed on specimens processed at 300 °C/s and 840 °C austenitization temperature with varying isothermal holding times (0 s, 40 s, and 120 s) to validate the accuracy of experimentally measured austenite fractions.

(iii) During the continuous heating process, the ratio of ferrite/austenite varies at different austenitization temperatures, resulting in significant variations in the transient microstructure with 0 s holding before isothermal formation. Therefore, specimens were heated to A_c1 + 30/70/110 °C at controlled rates of 1.78 °C/s, 50 °C/s, and 300 °C/s, followed by immediate quenching, as shown by the dotted line in Figure 1a, to obtain the transient microstructure before the isothermal austenite formation for subsequent formation analysis under various austenitization temperatures.

Based on the above investigation, the influence of heating rates on isothermal austenite formation kinetics was further investigated by employing three heating rates (1.78 °C/s, 50 °C/s, and 300 °C/s) to reach the same austenitization temperature (790 °C), followed by isothermal holding for 200 s, as illustrated in Figure 1b. At the same time, through continuous heating and immediate quenching to room temperature, the transient microstructure before the isothermal austenite formation was obtained to analyze its influence on the subsequent formation process under various heating rates, as indicated by the dotted line in Figure 1b.

2.3. Calculation of Experimental Isothermal Austenite Fraction

The experimental data on isothermal austenite formation kinetics were obtained by dilatometry and the lever rule [23,25,32]. Figure 2 schematically demonstrates the analytical procedure in which (a) is the dilatation–temperature curve and (b) is the dilatation–time curve (shared y-axis). Key features include (i) isothermal temperature line EG intersecting ferrite (E) and austenite (G) expansion extensions, with transformation initiation at F; (ii) horizontal reference lines (EA, FB, GD); (iii) time-dependent line AD, where segment lengths $L_{BC}$ and $L_{BD}$ enable calculation of the instantaneous isothermal austenite fraction $X_{\gamma \_iso}$ via Equation (1).

$$X_{\gamma \_iso}=(1-X_{\gamma \_non iso})\times (L_{BC}/L_{BD})+X_{\gamma \_non\_iso}$$

(1)

where $L_{BC}$ represents the austenite formation from the isothermal initiation (t = 0 s) to time t; $L_{BD}$ represents the total austenite formation from isothermal initiation (t = 0 s) to complete austenitization; $L_{BC}/L_{BD}$ represents the I nstantaneous austenite formation fraction exclusively during the isothermal stage at time t; and $X_{\gamma \_non\_iso}$ is the non-isothermal austenite formation fraction during continuous heating, which was experimentally determined for various heating rates and target temperatures in previous studies [15].

2.4. Microstructure Characterization

Furthermore, the microstructure of the specimens was examined by Scanning Electron Microscopy (SEM/ZEISS/ULTSTA 55) (ZEISS, Oberkochen, Germany). The electron type is secondary electron (SE), potential acceleration is 20 kV, probe current is 4 pA to 20 nA, and spot size is 1.0 nm. Observations were conducted on the TD plane (normal to the transverse direction) at the center of the heat-treated zone. The specimens for SEM were prepared by sanding and polishing sequentially with #200 to #2000 grit sandpaper and then polished and etched in 4% nital for 10 s.

3. Results and Discussion

3.1. Transient Microstructure Before Isothermal Holding Process

Figure 3 illustrates the initial microstructures of cold-rolled Q&P steel as observed by SEM. The microstructure of cold-rolled steel consists of deformed ferrite and pearlite, as shown in Figure 3a. The cold-rolled deformed pearlite is distributed in long strips along the rolling direction, featuring flat lamellar cementite and some spheroidized cementite within the pearlite, as depicted in Figure 3b.

As illustrated in Figure 4 and Figure 5, the transient microstructures before isothermal austenite formation were systematically characterized under various heat treatment conditions to investigate the intrinsic effects of austenitization temperature and heating rates. The micrographs reveal distinct phase distributions, with darker regions corresponding to ferrite and lighter areas representing martensite [18]. Specifically, Figure 4a–f present the transient microstructures for specimens heated at 1.78 °C/s, 50 °C/s, and 300 °C/s, respectively, to different austenitization temperatures, followed by immediate quenching without isothermal holding. As the austenitizing temperature gradually increases, ferrite continuously transforms into austenite, resulting in a decrease in the ferrite content in the transient microstructure before isothermal transformation when approaching A_c3. Meanwhile, a significant reduction in the ferrite recrystallization degree is observed in the transient microstructure with increasing heating rates, as demonstrated in Figure 5a,d,g.

Figure 5 shows the transient microstructure before isothermal austenite formation when different heating rates were applied to reach the same austenitization temperature (790 °C) with immediate quenching. A progressive decrease in the ferrite recrystallization degree is observed with increasing heating rates, manifested by increasingly flattened grain morphology, which is consistent with prior findings on non-isothermal recrystallization behavior [21].

3.2. Isothermal Austenite Formation Kinetics

3.2.1. Effect of Austenitization Temperature on Isothermal Austenite Formation Kinetics

For heating rates of 1.78 °C/s, 50 °C/s, and 300 °C/s, the influence of different austenitization temperatures on the isothermal austenite formation kinetics was studied under a certain heating rate. The experimental results of isothermal austenite formation kinetics were quantitatively determined via dilatometric analysis and lever rule application for various temperature–time combinations, as shown in Figure 6. The results reveal that (i) the rate of austenite formation initially increases and subsequently decreases with rising temperature at the same heating rate, and (ii) complete austenitization is achieved more quickly at the elevated temperatures.

At lower austenitization temperatures (e.g., 770 °C at 1.78 °C/s, 790 °C at 50 °C/s, 800 °C at 300 °C/s in Figure 6), the low thermodynamic formation driving force results in slower isothermal formation kinetics. Intermediate temperatures (810 °C at 1.78 °C/s, 830 °C at 50 °C/s, 840 °C at 300 °C/s) exhibit accelerated formation kinetics due to enhanced driving forces [30]. However, as temperatures approach A_c3 (850 °C at 1.78 °C/s, 870 °C at 50 °C/s, 880 °C at 300 °C/s), the depletion of available ferrite during continuous heating (Figure 4c,f,i) and reduction in retained strain energy [33] leads to progressively decreasing formation kinetics in the subsequent isothermal stage.

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation [26,27,28,29] was employed to calculate the austenite fraction to further study the isothermal austenite formation kinetics:

$$X_{\gamma \_iso}=1-\mathrm{e}\mathrm{x}\mathrm{p}(-k·t^n)$$

(2)

$$k=k_0\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{-Q}{RT}}\right)$$

(3)

Since the $k_0$ parameter of Equation (3) is a material constant related to the temperature variation in the material, when the temperature changes at the same heating rate, the model parameter $k$ also changes accordingly, thereby affecting the isothermal austenite volume fraction. This enables the description of the variation in isothermal austenite formation of the material at different temperatures with the holding time. In most studies on isothermal austenite formation, the JAMK equation has been used to describe this process [21,25,30].

Take logarithms on both sides of Equations (2) and (3):

$$\mathrm{l}\mathrm{n}\left(\mathrm{l}\mathrm{n}\left(1/\left(1-X\right)\right)\right)=n\mathrm{l}\mathrm{n}t+\mathrm{l}\mathrm{n}k$$

(4)

$$\mathrm{l}\mathrm{n}k={\displaystyle \frac{-Q}{RT}}{+\mathrm{l}\mathrm{n}k}_0$$

(5)

where $t$ is the austenitization duration, $T$ is the austenitization temperature, $n$ is the Avrami exponent, $k$ is a model parameter related to the nucleation and growth rate, sensitive to temperature, $k_0$ is a constant related to the material, $Q$ is the activation energy, and $R$ is the molar gas constant.

Equation (4) was linearized by plotting $\mathrm{l}\mathrm{n}\left(\mathrm{l}\mathrm{n}\left(1/\left(1-X\right)\right)\right)$ against $\mathrm{l}\mathrm{n}t$, where $n$ represents the slope and $\mathrm{l}\mathrm{n}k$ the intercept. The experimental austenite fraction calculated from Figure 6 was fitted to Equation (4), yielding the $n$ and $\mathrm{l}\mathrm{n}k$ values. As shown in Figure 7, the results of linear fitting demonstrate excellent agreement, confirming the applicability of the JMAK model for analyzing the isothermal transformation in the studied steel. Furthermore, $\mathrm{l}\mathrm{n}k$ exhibits a linear relationship with $-1/RT$, enabling determination of the $Q$ (slope) and ${\mathrm{l}\mathrm{n}k}_0$ (intercept) through Equation (5), as presented in Figure 8. The values of parameters $Q$, $n$, and $k_0$ are summarized in

Table 3. Parameters for the isothermal austenite formation kinetics model incorporating the heating rates.

Heating Rate (°C/s)	$\mathit{Q}$ (J·mol−1)	$\mathit{n}$	${\mathit{k}}_0$
1.78	327,796.79	0.227	3.606 × 1015
50	237,209.10	0.270	1.754 × 1011
300	210,500.63	0.417	8.768 × 109

.

The derived parameters ($Q$, $n$, and $k_0$) were utilized in the JMAK model to predict isothermal austenite transformation kinetics for specimens heated at 1.78 °C/s, 50 °C/s, and 300 °C/s to various austenitization temperatures, with results plotted against experimental data on a log10 scale in Figure 9. The conventional JMAK model demonstrates accurate predictive capability for isothermal austenite formation kinetics under a certain heating rate. However, the failure to incorporate heating rate effects restricts its multi-rate applicability.

3.2.2. Effect of Heating Rates on Isothermal Austenite Formation Kinetics

The influence of different heating rates on the isothermal austenite formation kinetics at the same austenitization temperature was investigated, with the specimens heated to 790 °C at heating rates of 1.78 °C/s, 50 °C/s, 100 °C/s and 300 °C/s, respectively. The experimental and model calculation results (Figure 10) reveal that at the same austenitization temperature, (i) the rate of isothermal austenite formation kinetics increases with heating rates, and (ii) the duration required for complete austenitization during isothermal process decreases significantly at higher heating rates.

For example, in Figure 10, when held at 790 °C for 0 s, the fraction of austenite obtained through ultrafast heating is lower than that through slow heating, which is attributed to the delayed effect of the austenite kinetics caused by the increased heating rate during continuous heating [21]. However, when the holding time is 5 to 10 s, an accelerated isothermal formation rate under ultrafast heating results in a higher austenite fraction compared to slow heating. When the holding time is extended to 900 s, in contrast with only a 73% austenite fraction of slow heating at 1.78 °C/s, complete austenitization is achieved at 300 °C/s, significantly shortening the process of complete austenitization. Previous studies [11] have established that the process with increased heating rates results in reduced ferrite recrystallization, as evidenced by the transient microstructures shown in Figure 5. Moreover, under slow heating conditions, recovery occurs first, followed by extensive recrystallization, leading to the release of substantial retained strain energy and dislocations. In contrast, rapid heating results in the simultaneous occurrence of recovery and recrystallization and an extremely short heating time, thereby retaining considerable retained strain energy and providing abundant dislocation sites for nucleation [34]. Consequently, higher heating rates lead to greater retained strain energy, thereby enhancing the driving force for isothermal austenite formation and accelerating the formation.

Subsequently, microstructural evolution was characterized for specimens heated at 300 °C/s to 840 °C with holding times of 0 s, 40 s, and 120 s, demonstrating a significantly accelerated rate of isothermal austenite formation kinetics at high heating rates. As shown in Figure 11, the specimen held for 0 s contained a 58% fraction of martensite (representing high-temperature austenite), while those held for 40 s and 120 s exhibited complete martensite without ferrite, confirming full austenitization within remarkably reduced timeframes.

3.3. Isothermal Austenite Formation Kinetics Model Incorporating the Heating Rates

Analysis of the parameters $Q$, $n$, and $k_0$ in Table 3 reveals distinct correlations with the heating rate, as shown in Figure 12a, which supplements the parameter values for isothermal austenite formation kinetics at heating rates of 15 °C/s and 150 °C/s. The activation energy $Q$ decreases with the increase in heating rates, which can be attributed to the reduced ferrite recrystallization in the transient microstructure before isothermal austenite formation at elevated heating rates. The resultant accumulation of retained strain energy enhances the driving force for austenite formation, thereby lowering the transformation activation barrier and facilitating austenite nucleation [33]. The Avrami exponent $n$ demonstrates a monotonic increase with heating rate (Figure 12b), attributable to its role as a growth dimensionality parameter [35]. The enhanced driving force for austenite formation at elevated heating rates promotes accelerated nucleation and growth kinetics, consequently elevating the $n$ value. The constant $k_0$ exhibits a progressive decrease with increasing heating rates, as illustrated in Figure 12c. This observed trend likely represents a compensatory adjustment corresponding to the variations in both $Q$ and $n$, though its underlying physical mechanism requires further systematic investigation.

Therefore, this paper proposes an expression to describe the variation in parameters $Q$, $n$, and $k_0$ with heating rate, as shown in Equation (6):

$$Par=b_1+b_2\times (1-\mathrm{e}\mathrm{x}\mathrm{p}(-b_3\times {\nu }^m\left)\right)$$

(6)

where $Par$ represent the $Q$, $n$, or $k_0$; $\nu$ is the heating rate; $b_1$, $b_2$, $b_3$ are model parameters, and $m$ is the power exponent of the model, determined through optimal prediction of the $Par$—$\nu$ relationship, with the corresponding prediction results presented in Figure 12.

In the above study, the relationship between $X_{\gamma \_iso}$ and $\nu$ was established by analyzing the variation of $Q$, $n$, and $k_0$ with $\nu$, thereby developing a heating-rate-dependent modified JMAK model during isothermal austenite formation. The model is composed of Equations (2), (3), and (6), with the relevant parameters summarized in

Table 4. Parameters for the heating-rate-dependent modified JMAK model.

$\mathit{P}\mathit{a}\mathit{r}$	${\mathit{b}}_1$	${\mathit{b}}_2$	${\mathit{b}}_3$	${\mathit{n}}_1$
$Q$ (J·mol−1)	428,000	−224,000	0.485	0.350
$n$	0.277	0.3	0.003	1
$k_0$	3,900,000	−3,899,991	0.034	1.455

.

Additionally, the isothermal austenite formation kinetics under the heating rates of 25 °C/s and 100 °C/s were experimentally measured and predicted to verify the accuracy of the model’s predictions. Figure 13a,b present comparative validation studies, where the experimental isothermal austenite formation kinetics of Q&P steel at various austenitization temperatures are systematically compared with predictions from the heating-rate-dependent modified JMAK model. A good agreement is observed between the experimental and predicted formation kinetics, demonstrating that the proposed modified JMAK model accurately describes the isothermal austenite formation behavior, even under varying heating rates before isothermal treatment. Compared to the conventional JMAK model, the modified model accounts for the influence of heating rates, thereby improving the prediction accuracy and extending the applicability of the model for isothermal austenite formation kinetics.

4. Conclusions

This study conducted an investigation into the effect of heating rates on the isothermal austenite formation kinetics of quenching and partitioning (Q&P) steel. Through experimental characterization of microstructural evolution and the development of models, the isothermal austenite formation behavior and kinetics variations under different heating rates were analyzed. The foldlowing conclusions can be drawn from this study:

(i) The rate of austenite formation initially increases and subsequently decreases with rising temperature from A_c1 to A_c3 at the same heating rate, and complete austenitization is achieved more quickly at elevated temperatures.

(ii) At the same austenitization temperature, the isothermal austenite formation rate increases with heating rates, and the time required for complete austenitization during isothermal process decreases significantly at higher heating rates. Such an acceleration effect is attributed to the inhibited ferrite recrystallization and consequent accumulation of retained strain energy at higher heating rates, thereby enhancing the driving force for isothermal austenite formation.

(iii) The experimental results revealed that both the transformation activation energy ($Q$) and material constant ($k_0$) decreased with increasing heating rates, while the Avrami exponent ($n$) showed a progressive increase.

(iv) A heating-rate-dependent modified JMAK model was established. The model accurately characterizes the effect of varying heating rates on isothermal austenite formation kinetics, enabling kinetic curves prediction under multiple heating rates and austenitization temperatures and overcoming the limitation of single heating-rate prediction in existing models, with significantly broadened applicability.