Effect of Cold-rolling and Heating Rate on Austenite Formation in a Low–Carbon Steel

Abstract

The austenite formation kinetics of a low–carbon steel under two initial conditions—annealed and cold–rolled (0.08C–1.22Mn–0.73Si) were determined by dilatometric analysis during continuous heating. In both conditions, the austenite formation occurred in two stages. The critical transformation temperatures are a function of the heating rate but not of the initial microstructure (annealed or cold–rolled) that is, for a given heating rate (0.06, 0.36, or 0.66 K s⁻¹), the critical transformation temperatures are similar for both conditions, despite in the cold–rolled condition, the cementite is spheroidized prior the austenite formation. The volume fraction of austenite was fitted based on the Johnson–Mehl–Avrami–Kolmogorov model to calculate the kinetics parameters k and n. The parameter k is proportional to the heating rate, and n changes between stages and heating rates for both conditions suggesting variations in the nucleation mode. The austenite–formation rate was calculated as a function of the microstructural evolution and transformation time. The austenite formation rate in the first stage is lower in the cold–rolled steel, during a specific range of temperatures, than in annealed steel which presented a formation rate maximum at a peak temperature. In the second stage, the behavior was similar for both conditions with a peak at the rate maximum.

1. Introduction

Austenite formation and ferrite recrystallization during continuous annealing of cold–rolled low–carbon steels are the main processes controlling the microstructure and final mechanical properties of steels during heat treatment. These processes can occur simultaneously or successively and can influence the transformation kinetics of subsequent phases. For instance, in the case of dual–phase steels with cold–rolled microstructures, an inter–critical anneal heat treatment, followed by quenching, is necessary. During heating and isothermal holding at the inter–critical temperature, the recrystallization and austenite formation could be overlapped. Later, during quenching, martensite is formed from the previously formed austenite, leading to a microstructure of ferrite and martensite, where an optimal strength–ductility ratio can be obtained.^1,2,3,4,5) To study the mechanisms involved in detail, it is necessary to separate the austenite formation and the recrystallization during inter–critical annealing.

Austenite formation during continuous heating has been widely investigated especially in low–carbon steels.^6,7,8,9,10) The process can occur in two transformation stages: 1) the decomposition of pearlite and 2) the transformation of ferrite. The kinetics of austenite formation depend on the chemical composition, initial microstructure, and heating rate.⁶⁾ The initial microstructure is one of the variables of greatest interest. This is mainly due to the variety of microstructures and morphologies with which the austenite formation process can occur.^11,12,13)

In cold–rolled low–carbon steels, austenite formation involves recrystallization of the cold-rolled microstructure, which modifies the evolution of austenite as a function of heating rate.^14,15,16) Liu et al.¹⁴⁾ reported that when the heating rate is low (~0.5 K s⁻¹), recrystallization is completed before reaching the austenite formation start temperature (Ac_1s). By employing a considerably high heating rate (~300 K s⁻¹), recrystallization overlaps during the austenite formation. In typical heating cycles for austenitizing or inter–critical heat treatment, a heating rate greater than 1 K s⁻¹ is used, so that the interaction between the recrystallization process and austenite formation is possible, which implies changes in the transformation and recrystallization mechanisms as well as the nucleation of new grains of ferrite and austenite on the cold-rolled microstructure.^17,18,19,20) However, the transformation processes at very low heating rates could differ from what is expected mainly due to the alloying elements and consequently, the critical transformation temperatures.^3,14) Exist evidence that alloying elements could cause the formation of spheroidal cementite during continuous annealing at very low heating rate due to the fragmentation of lamellar pearlite and dislocation density generated by the cold–rolling process.^{2,10,14,18,21)} Considering that one of the factors that influences on the formation of austenite is the initial microstructure (phases, size and morphology), it is important to determine the contribution of spheroidal cementite on the transformation kinetics. The aim of this work is to study the effect of the initial cold–rolling microstructure and heating rate on the kinetics of austenite formation during continuous heating.

2. Experimental Procedure

2.1. Material

Cylindrical solid bars were machined (15 mm in diameter and 150 mm in length) from an annealed low–carbon steel (19 mm section) as a commercial wire rod. The chemical composition of the steel is shown in Table 1 as obtained by elemental analysis with a GDS–400A (Leco, EE. UU) glow discharge spectrometer.

Table 1. Chemical composition of low carbon steel (% wt.).

%C	%Mn	%Si
0.081	1.228	0.731

The bars were cold–rolled in an 800–kN semi–industrial rolling mill (Hille, England) with a 0.5 mm pass reduction at a constant speed of 180 rpm until reaching a total reduction percentage of 60%.

The initial microstructure of the steel (in annealed condition) and the microstructure after cold-rolling were characterized by scanning electron microscopy. Samples were taken from the bars in its longitudinal section. These were prepared by grinding with sandpaper: SiC thin (16 μm) to very fine (8 μm). The samples were then polished with alumina 0.3 μm and then with a suspension of colloidal silica 50% by volume. The samples were observed with a JSM-5910 LV scanning electron microscope (JEOL, USA). The grain size was determined according to the ASTM E–112 standard, while the phase distribution was calculated using the Image J open source analysis package.

2.2. Differential Thermal Analysis

For the dilatometric analysis, cylindrical specimens (5 mm in diameter and 15 mm in length) were machined in their two conditions (annealed and cold–rolled). Differential dilatometry was performed on a vertical dilatometer L75 V (Linseis, Germany). The contact surfaces of the specimens were prepared by grinding and polishing to obtain uniform and parallel surfaces in order to reduce the roughness of the contact area. To study the effect of cold–rolling and heating rate on the austenite formation kinetics, the specimens were tested at low heating rates: 0.06, 0.36, and 0.66 K s⁻¹ from a preheating temperature of 308 K. For each heating rate, a temperature of 1323 K was reached and subsequently, each specimen was cooled at a rate of 0.33 K s⁻¹ until room temperature. To determine the degree of recrystallization before the start of austenite formation, other different cold-rolled specimens were tested under the same conditions (heating rate and preheating temperature) up to a temperature of 965 K (below the respective critical transformation temperature Ac_1s), and then quenched. The specimens were prepared like the previous specimens to reveal and analyze the microstructure with a BMX60M light microscope (Olympus, Japan).

3. Results and Discussion

3.1. Microstructure

The microstructure of the annealed condition is composed of ferrite (F) and pearlite (P) (Fig. 1(a)) (volume fraction of ferrite 0.87 ± 0.08) with an ASTM No. 9 grain size as well as an average Vickers microhardness of 157.2 ± 17.4 HV0.2/15 in cross–section. In Fig. 1(b), the microstructure in the cold–rolled condition consists of deformed ferrite and pearlite, although the pearlite shows less deformation due to cementite strength. The microhardness increased by 47% (295.7 ± 12.1 HV0.2/15) due to the generation of dislocations. The standard deviation of the average microhardness values indicate that the microhardness remains uniform throughout the cross–section ensuring the homogeneity of the microstructure.

Fig. 1.

Initial microstructure for the (a) annealed condition and (b) cold–rolled condition. F: ferrite and P: pearlite.

3.2. Dilatometry

Figure 2 shows the dilatometric curves at different heating rates for the specimens in annealed and cold–rolled conditions. The ε_d denotes the dilatation strain of the specimen during thermal cycle, and dε_d/dT refers to the first derivative of dilatation strain as a function of temperature. The dilatation strain is the relation between length change and initial longitude of the specimen. The effect of cold–rolling and heating rate on the critical transformation temperatures and the extent of the transformation zone is also observed. The critical transformation temperatures are displaced at higher temperatures as heating rate increase for the two conditions. These critical transformation temperatures, and the overheating (ΔT, defined as the difference of Ac_1s and the equilibrium temperature Ae₁ as calculated from the Andrews equation²²⁾), are indicated in Table 2. ΔT increases as the heating rate increases thus generating a greater contribution of energy to austenite formation. The time to reach the transformation zone decreases as the heating rate increases; this in turn leads to low carbon diffusion and an increased critical transformation temperature that delays austenite formation. Furthermore, there is no significant change in ΔT due to cold–rolled condition regardless of the heating rate because the values are similar.

Fig. 2.

Dilatometric curves at different heating rates (a) 0.06, (b) 0.36, and (c) 0.66 K s⁻¹ for the annealed (ANN) condition and cold–rolled (CR) condition.

Table 2. Critical transformation temperatures of austenite formation Ac_1s, Ac_1f and Ac₃.

Condition	HR K s−1	Ac1s K	Ac1f K	Ac3 K	ΔT=Ac1s−Ae1 K
ANN	0.06	1015.85	1067.75	1215.65	11.07
	0.36	1036.65	1082.15	1217.65	31.87
	0.66	1072.05	1117.75	1227.50	62.27
CR	0.06	1014.55	1072.93	1217.45	9.77
	0.36	1041.15	1090.05	1214.25	36.37
	0.66	1065.88	1119.28	1224.80	61.09

Austenite formation in low carbon steels may occur in two stages:^{6,8,9,12,13,23,24)} firstly, by the decomposition of pearlite and secondly by the transformation of ferrite. These stages can be seen in the derivative curve (Fig. 2), as follow: the first contraction, delimited by the temperatures Ac_1s and Ac_1f, corresponds to the decomposition of pearlite. The second contraction between the temperatures Ac_1f and Ac₃ indicates the transformation of ferrite into austenite. The effect of cold–rolling on the dilatometric behavior can be seen during the first contraction, where the minimum of the dε_d/dT curve is softer in the cold-rolled condition than in the annealed condition. The second contraction tends to behave similarly as the heating rate increases. This indicates that the effect of cold–rolling remains mainly on the first stage of austenite formation without significantly affecting the critical transformation temperatures (Figs. 2(a)–2(c)). As a function of heating rate, the austenite formation can occur in two different ways: 1) at low heating rates, recrystallization occurs before reaching the critical transformation temperature Ac_1s; therefore, pearlite decomposition occurs from a recrystallized microstructure, and 2) at high heating rates, the recrystallization as well as pearlite decomposition developed simultaneously.^{14,17,19,20,25)}

3.3. Continuous Heating Transformation (CHT) Diagram

Figures 3(a)–3(b) shows the CHT diagrams for annealed condition and cold–rolled condition of the low–carbon steel. Critical transformation temperatures are superimposed on the heating paths providing an overview of the transformation zones as well as the phases and microconstituents. Below the temperature line Ac_1s, the zone is associated with the initial microstructure of ferrite and pearlite (F + P). Above this line, the field is associated with the pearlite decomposition zone (delimited by the temperature lines Ac_1s and Ac_1f) which is related to the first stage, where ferrite, pearlite, and austenite (F + P + A) are presented. After this zone is the second stage denominated as the inter-critical zone where ferrite transforms into austenite (F + A). Finally, the austenitic field is noticeable above the temperature Ac₃. The critical transformation temperatures increase when the heating rate increases mainly causing a slight contraction of the inter–critical zone. Thus, not all temperatures are affected by the heating rate because the temperature Ac₃ remains practically constant for both diagrams. Although there is a particular effect of cold–rolling on austenite formation kinetics, there is no clear evidence of impact on the formation temperatures and transformation stages.

Fig. 3.

Continuous heating transformation diagrams for low–carbon steel at different heating rates: 0.06, 0.36 and 0.66 K s⁻¹ for (a) annealed condition and (b) cold–rolled condition.

3.4. Austenite Formation Kinetics

The transformation degree was determined using the lever rule and the extrapolation and regression line intersection method as part of the austenite formation kinetics analysis. In addition, the transformation zone was divided by stages for each microstructural condition and heating rate. Figures 4(a)–4(c) shows the microstructural evolution of austenite during the first stage. A delay in the transformation degree is observed from a heating rate of 0.36 K s⁻¹, which becomes more evident for the heating rate of 0.66 K s⁻¹. Unlike annealed condition, the transformation degree of cold–rolled condition does not present a completely sigmoidal shape, especially in the final part of the curve, which remains practically linear. It seems that the transformation stage is controlled by an increasing nucleation mechanism associated with a possible microstructure refinement.²⁵⁾ In this instance, the austenite growth rate initially increases and remains almost constant until the transformation is complete (for the first stage of austenite formation). This trend may be due to morphological factors associated with the recovery and recrystallization process of the ferrite grains a priori to the transformation zone.

Fig. 4.

Austenite formation degree in annealed condition and cold–rolled condition at different heating rates: (a) 0.06, (b) 0.36 and (c) 0.66 K s⁻¹, for the first stage.

To elucidate the effect of recrystallization on the austenite formation, some cold-rolled specimens were tested under the same conditions, but until reaching 963 K (below critical transformation temperature Ac_1s) and then quenched.

Figure 5 shows the initial microstructure in the annealed condition together with the normal distribution of the ferritic grain size, and Table 3 shows the mean ferritic grain size (G_α), the coefficient of skewness (γ₁), the coefficient of kurtosis (γ₂) and microhardness. The mean ferritic grain size is G_α=9.89 with a standard deviation of μ=0.97 indicating that most of the microstructure (64%) has a grain size between 8.92 and 10.86. Based on the parameters γ₁ and γ₂, which are associated with the asymmetry of the curve and the concentration grade of the grain size, respectively, a certain asymmetry is appreciated that generates the slightly positive skewness to larger grains. When γ₁, γ₂→0, a completely symmetric normal distribution is presented with a higher concentration in the mean and a minimum standard deviation. These conditions are optimal that can be expected in a microstructure with a completely homogeneous grain size. This does not occur in the case of steel in annealed condition because there is a certain dispersion that generates a heterogeneous distribution in G_α.

Fig. 5.

(a) Microstructure and (b) grain size distribution in the annealed condition.

Table 3. Ferritic grain size of the annealed condition microstructure.

Gα ± μ	Gα ± μ %	HV0.1/15	γ1	γ2
9.89 ± 0.97	64.0	157.21 ± 17.43	0.05	−0.36

Figures 6(a)–6(c) shows the microstructures and the normal distribution of grain size after continuous heating up to 965 K of the 60% cold–rolled specimens, as a function of the heating rate. The first observation is that the ferrite is completely recrystallized before reaching the critical transformation temperature Ac_1s, that means, at the heating rates studied, recrystallization and austenite formation are two separate processes. But, in Fig. 4(c), it is observed that in the cold–rolled steel there is a delay in the austenite formation, compared to the annealed steel. This means that although the ferrite is recrystallized before the start of austenite formation (for the 60% cold–rolled steel), there is an effect of cold–rolling on the transformation. In same figure, it can be seen two main differences, with respect to the annealed condition: 1) the refinement of the ferritic grain, which changes from 9.89 (for the annealed condition) to 11.53, 10.92 and 11.20 for each heating rate employed (Table 4) and 2) the cementite of the pearlite has been spheroidized. Although the cementite is spheroidized under the three different heating rates, it is observed that for the heating of 0.66 K s⁻¹ the cementite is concentrated in the original location of the pearlite (Fig. 6(c)). For samples heated at slower heating rates, the cementite is more dispersed in the ferritic grains (Figs. 6(a)–6(b)).

Fig. 6.

Microstructure and ferrite grain size distribution of 60% cold-rolled specimens and continuous heating until 965 K with a heating rate of (a) 0.06, (b) 0.36 and (c) 0.66 K s⁻¹.

Table 4. Ferritic grain size and microhardness under cold–rolled and continuous annealing at different heating rates and annealing temperatures.

HR K s−1	TANN K	Gα ± μ	Gα ± μ %	HV0.1/15	γ1	γ2
0.06	965	11.53 ± 1.65	65.3	139.13 ± 7.69	0.07	−0.67
0.36	965	10.92 ± 1.12	66.2	142.11 ± 5.68	−0.04	−0.53
0.66	965	11.20 ± 1.13	64.0	147.65 ± 4.73	0.09	−0.47

Cold–rolling is known to accelerate spheroidization kinetics,²⁷⁾ but it is also known that the kinetic of austenite formation is delayed when spheroidized cementite is presented before the start of the transformation.¹⁰⁾ For a steel with an annealed initial microstructure of ferrite and pearlite, Huang et al.¹⁰⁾ indicate that at low heating rates, the formation of austenite (nucleated in the pearlite) is favored. For higher heating rates, further nucleation is promoted at ferrite grain boundaries. This effect is observed in annealed steel (Figs. 4(a)–4(c)) where it can be seen that the faster the heating rate, the shorter the time to complete austenite formation in stage 1. For cold–rolled steel the same behavior is also observed, although at the higher heating rate (0.66 K s⁻¹) there is a delay in the austenite formation with respect to annealed steel. It is known that the interfacial energy of spheroidized cementite is less than that associated with cementite plate-shaped lamellae, which would explain the delay in austenite formation.

Figures 7(a)–7(c) presents the second stage in the annealed and cold–rolled condition. Unlike the first stage, a very similar behavior is observed for both conditions. Likewise, the transformation time decreases as a function of the heating rate.

Fig. 7.

Austenite formation degree under annealing and cold–rolled conditions at different heating rates: (a) 0.06, (b) 0.36, and (c) 0.66 K s⁻¹ for the second stage.

The austenite formation kinetics for each stage and microstructural condition was analyzed through the kinetic parameters associated with the nucleation and growth mechanisms using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model. Despite the fact that the model describes the transformation degree under isothermal conditions, it has been used to evaluate the non–isothermal kinetic parameters and obtain an interpretation of the transformation mechanisms^24,25,28) through the nucleation rate laws proposed by Cahn.²⁹⁾ Here, the transformation degree was adjusted using the JMAK nonlinear model:   

$$X_{\gamma }=1-exp\left(k\cdot t^n\right)$$(1)

Here, X_γ is the volume fraction of austenite, t is the transformation time, and k and n are the kinetic parameters associated with the nucleation and growth mechanisms. Table 5 shows the kinetic parameters of the JMAK model for the annealing and cold–rolled conditions as a function of the heating rate. In general, the approximations agree with respect to the data calculated using the lever rule (Figs. 4 and 7) according to the determination coefficient these coefficients were above 0.99 for the first stage and 0.98 for the second stage. Parameter n increases due to the heating rate regardless of the stage or the microstructural condition and also changes in magnitude between one stage and another at the same condition, which denotes a change in the transformation mechanism mainly in the nucleation mode. This is to be expected because nucleation occurs between the boundary of the ferrite and spheroidized cementite in the first stage. In the second stage, it occurs at the grain boundary of the ferrite. However, the change of n between stages is different for both conditions.

Table 5. Values of kinetic parameters for the JMAK equation at heating rates of 0.06, 0.36, and 0.66 K s⁻¹ for annealed and cold–rolled conditions.

Condition	HR K s−1	Stage I			Stage II
		kI	nI	R2	kII	nII	R2
ANN	0.06	2.03E-06	2.1337	0.9959	1.96E-09	2.7400	0.9855
	0.36	1.70E-05	2.4697	0.9966	8.97E-08	2.9746	0.9906
	0.66	1.44E-05	2.9067	0.9992	6.81E-07	2.9884	0.9866
CR	0.06	1.24E-05	1.8308	0.9925	1.69E-09	2.7705	0.9846
	0.36	1.52E-05	2.4610	0.9945	6.20E-08	3.0221	0.9861
	0.66	3.07E-05	2.5512	0.9946	2.33E-07	3.2140	0.9864

According to the nucleation rates laws in grain boundaries proposed by Cahn,²⁹⁾ parameter n is related to the preferential site and nucleation rate. Nucleation occurs at the grain face, edge, or corners when the value of n = 1, 2, or 3, respectively. Regarding the nucleation rate, values of n between 1 and 3 indicate a nucleation rate equal to zero. This is because all nucleation sites are present when the transformation begins; thus, the formation of the new phase depends solely on the number of sites and growth rate, this condition is called site saturation. On the other hand, if 3 < n < 4, then the nucleation rate is decreasing. The nucleation rate is constant if n = 4, and the nucleation rate is increasing if n > 4. Based on the foregoing and Table 5, it is interesting that parameter n changes from 2.1 to 2.9 during the first stage for the annealed material; the preferential nucleation site could be interpreted to occur at the boundary and subsequently at the grain corners as the heating rate increases with a nucleation mode of site saturation. In the second stage, parameter n approaches ~3 as the heating rate increases, which suggests that there is no significant change in the transformation mechanism. In this case, the transformation mechanism changes from the first to the second stage where the austenite growth is controlled by carbon diffusion. According to Christian,³⁰⁾ growth occurs from small particles with increasing nucleation rate for n > 2.5. In this case, the nucleation mode corresponds to a mixture nucleation that agrees with Mittemeijer²⁶⁾ and could represent the weighted sum between continuous and site saturation nucleation modes.

In comparison, in the cold–rolled steel, a variation in the parameter n from 1.8 to 2.5 is observed during the first stage by augmenting the heating rate from 0.06 to 0.66 K s⁻¹. Unlike annealed steel, parameter n is slightly lower and approaches a value of 2.5. These differences could be associated with the spheroidizing processes especially at values where the heating rate is 0.66 K s⁻¹. In this situation, the parameter n is lower compared to annealed steel.

In the second stage, for the annealing condition, parameter n changes slightly (Table 5), but for the cold–rolled condition, this parameter is ~2.7 at the heating rate of 0.06 K s⁻¹ (very similar to the annealing condition), and increases up to 3.2 as the heating rate increases. In the cold–rolled condition, n does not approach a fixed value as in the annealed condition probably due to decomposition of spheroidized cementite during the first stage. This causes the number of nucleation sites to increase. Hence, the value of n does not approach a fixed value even though the transformation mechanism is the same during the second stage.

Departing from the transformation kinetics, there are certain transformation mechanisms that are affected during austenite formation especially in the first stage; hence, analyzing the total austenite volume fraction and the transformation rate it is observed an abnormal behavior. The total austenite volume fraction $X_{\gamma }^T$ could be obtained from the austenite volume fraction in each stage ($X_{\gamma }^{Stg-I}$ and $X_{\gamma }^{Stg-II}$) as well as the initial pearlite volume fraction ($X_P^i$) and the initial ferrite volume fraction ($X_{\alpha }^i$):²⁴⁾   

$${\mathrm{X}}_{\gamma }^{\mathrm{T}}={\mathrm{X}}_{\gamma }^{\mathrm{S}\mathrm{t}\mathrm{g}-\mathrm{I}}\cdot {\mathrm{X}}_{\mathrm{P}}^{\mathrm{i}}+{\mathrm{X}}_{\gamma }^{\mathrm{S}\mathrm{t}\mathrm{g}-\mathrm{I}\mathrm{I}}\cdot {\mathrm{X}}_{\mathrm{\alpha }}^{\mathrm{i}}$$(2)

And the total transformation rate can be approximated by:   

$$\frac{\mathrm{d}{\mathrm{X}}_{\gamma }^{\mathrm{T}}}{\mathrm{d}\mathrm{t}}\approx \frac{\mathrm{\Delta }{\mathrm{X}}_{\gamma }^{\mathrm{T}}}{\mathrm{\Delta }\mathrm{t}}$$(3)

Here, the austenite formation rate is equivalent to the difference between the volume fractions of austenite concerning the acquisition time interval.

Figures 8(a)–8(c) shows the behavior of the total transformation rate as a function of temperature for both microstructural conditions highlighting two peaks that represent the points of maximum transformation rate for each stage. These peaks displace to higher temperatures both due to the heating rate and the microstructural condition. The transformation rate for the annealing condition is greater during the first stage, which subsequently decreases with respect to the cold–rolled condition. Similarly, the behavior of the formation rate curve tends to be very similar for both conditions at a low heating rate in where there is a delay during the second stage for the cold–rolled condition (Fig. 8(a) in contrast to Figs. 8(b) and 8(c)). This could be because the rate is so low that it tends towards equilibrium; thus, the variations in the transformation rate are exclusively due to the grain refinement of the cold–rolled microstructure. In addition, spheroidized cementite is present during the first stage as observed in continuous annealing. In agreement with the analysis of grain size distribution and the transformation degree it is inferred that this behavior might be due to microstructural variations prior to transformation with respect to the size and homogeneity of the grain as well as the effect of spheroidized cementite. The temperatures where the maximum transformation rate occur are very similar because the heating rate increases regardless of the microstructural condition for both stages.

Fig. 8.

Austenite formation rate as a function of temperature at different heating rates: (a) 0.06, (b) 0.36, and (c) 0.66 K s⁻¹.

3.5. Activation Energy

Activation energies were calculated using the Kissinger method³¹⁾ using the transformation rate in stages and the heating rate (cf. Fig. 8). From the transformation rate curves, the peak temperatures, corresponding to the points of maximum transformation rate at a specific fraction of formation, were determined. The method considers these parameters assuming continuous conditions with constant heating rate values according to the following equation:²⁸⁾   

$$ln\left(\frac{T_{P-i}}{\phi }\right)=\frac{Q_i}{R{T}_{P-i}}+ln\left(\frac{Q_i}{R{k}_0}\right)+\alpha$$(4)

Where T_P–i is the peak temperature corresponding to the point of maximum transformation rate at a specific fraction of austenite formation (X_γ) for the stage i, φ is the heating rate Q_i is the activation energy for the stage i, R is the universal gas constant, k₀ is a pre-exponential factor of the kinetic constant k, and α is a constant that depends on the degree of transformation. Table 6 indicates the parameters used in the Eq. (4) to calculate activation energy in stages. The activation energies in stages are calculated from the slope of the straight line that is generated when plotting ln(T_P–i/φ) vs 1/RT_P–i. Table 7 shows the apparent activation energies for each of the stages in the annealed and cold–rolled conditions.

Table 6. Parameters to determine the activation energies by the Kissinger method in stages for the annealing and cold-rolled conditions.

Condition	HR K s−1	TP–I K	$ln\left(\frac{T_{P-I}^2}{\phi }\right)$	$\frac{1}{R{T}_{P-I}}$	TP–II K	$ln\left(\frac{T_{P-II}^2}{\phi }\right)$	$\frac{1}{R{T}_{P-II}}$
ANN	0.06	1036.55	16.61	1.160E-4	1177.65	16.86	1.021E-4
	0.36	1060.15	14.94	1.134E-4	1178.95	15.15	1.020E-4
	0.66	1094.25	14.40	1.099E-4	1197.55	14.58	1.004E-4
CR	0.06	1050.90	16.63	1.144E-4	1181.00	16.87	1.018E-4
	0.36	1072.30	14.96	1.122E-4	1181.15	15.15	1.018E-4
	0.66	1101.20	14.41	1.092E-4	1198.40	14.58	1.004E-4

Table 7. Activation energies for annealed and cold-rolled conditions.

Condition	First stage $\frac{Q_I}{{\text{kJ mol}}^{-\text{1}}}$	Second stage $\frac{Q_{II}}{{\text{kJ mol}}^{-\text{1}}}$
ANN	347.70	917.53
CR	413.05	976.26

In the case of the first stage, the activation energies are 347 and 413 kJ mol⁻¹ for the annealed and cold–rolled condition, respectively. These values are higher than the values reported for the diffusion of carbon in austenite (250 kJ mol^{−1 32,33)}). The increase in activation energy could be due to the alloying elements and the initial microstructure, since it has been reported that the initial microstructure influences the activation energy. For example, an activation energy of 366 kJ mol⁻¹ has been reported for a microalloyed steel with a ferritic microstructure during the first stage of austenite formation.¹²⁾ In similar systems (chemical composition, microstructure, heating rate), the activation energies corresponding to the second stage have not been reported. For austenite formation calculated from the total volume fraction, Ollat et al.²⁾ reported an activation energy of 900 kJ mol⁻¹ from two different initial microstructures: 1) recrystallized ferrite plus spheroidized cementite and 2) ferrite and deformed pearlite. These values are close to those obtained in this study in the second stage (Table 7), however, due to their high magnitude, these values have no physical justification related to the transformation mechanism.

4. Conclusions

Austenite formation kinetics were investigated in annealed and cold–rolled low–carbon steels by dilatometric analysis. The critical transformation temperatures were not modified by the microstructural conditions and only increased with heating rate. Despite this, differences were observed when analyzing the transformation degree during the first stage.

This work analyzed the ferrite distribution and grain size during continuous annealing. For all heating rates, before austenite formation, the following microstructural characteristics were observed: a) ferritic grain refinement, b) homogeneity of the ferrite and c) spheroidization of the cementite. In contrast to the first stage, very similar behavior was observed during the second stage.

According to the kinetic analysis, changes in magnitude were observed in the parameter n between the austenite formation stages as a function of the heating rate and the microstructural conditions. These were associated with the transformation mechanisms mainly due to the nucleation mode where austenite formation occurs in each of the stages.

In addition to the austenite formation rate curves, there were two peaks that represent the maximum transformation rate points of each stage intrinsic to low–carbon steels. These are displaced at higher temperatures both peaks via the heating rate as a microstructural condition; the transformation rate for the annealing condition was greater during the first stage with a tendency to subsequently decrease with respect to the cold–rolled condition. This emphasizes the variations in the transformation mechanisms.

The activation energy is susceptible to the initial microstructure prior to the austenite formation. In the cold–rolled condition, the activation energy is greater than in the annealed condition, justifying the delay in the kinetics of austenite formation.

Acknowledgements

I. Alanis–Fuerte would like to thank the National Council of Science and Technology of Mexico (CONACYT) for the Ph.D. scholarship (No. 722914) received. The authors also are grateful to CONACYT for the use of the equipment acquired with support for the projects No. 235780, 271878 and 282357 of the National Laboratory SEDEAM–CONACYT.

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