Hot-Deformation Behavior and Processing Maps of a Low-Carbon Fe-2 wt% Nb Steel

: In the present work, the deformation behavior and processing maps of a low-carbon Fe-2 wt% Nb steel were studied by means of hot-compression tests at temperatures of 800–1150 ◦ C and strain rates of 0.01–10 s − 1 . The hot-processing maps at different strains and corresponding microstructural evolution were constructed and discussed. The hot-deformation behaviors of two different phase regions, i.e., austenite + NbC dual-phase and ferrite + NbC dual-phase, were predicted by determining the constitutive equations using Arrhenius-type and Zener–Hollomon models. The results suggest that the hot-deformed microstructures of the material present a strong correlation with the processing parameters in the hot-processing maps. In addition, the optimum parameters based on the processing maps were obtained, and the instable and the safe domains during the hot deformation in the hot-processing maps provide solid theoretical guidance for industrial production.


Introduction
Heat-resistant steels with outstanding high-temperature properties are necessary in thermal power plants [1][2][3], turbo-chargers [4], and pressure vessels [5]. In our previous study, we designed a low-carbon 2 wt% Nb bearing steel, in order to utilize NbC precipitates with various sizes to stabilize and strengthen the microstructures at both room temperature and high temperatures [6]. We found that the yield stress and ultimate tensile stress of the as-forged 2Nb steel were 297 MPa and 430 MPa at 600 • C, which shows an excellent potential for future application [6]. However, to further improve both the strength and ductility, there are still several things that need systematic investigations, including the hot-deformation behavior and processing maps, which is the first step for microstructural control [7].
Understanding the high-temperature deformation mechanism, constructing a constitutive model and grasping the law of the microstructural evolution of metals play significant roles in optimizing the hot-process parameters for high-quality products of alloys [7][8][9].
In this study, we investigated the hot-deformation behavior of Fe-2 wt% Nb steel by fitting processing parameters and establishing constitutive equations in detail. Based on the above data calculation and model establishment, a hot-processing map was established, which can provide a reliable and accurate strain-processing area, to predict hot-deformation behavior and guide manufacturing and processing.
As shown in Figure 1, which was calculated and drawn using the Thermocalc software (Thermo-Calc 2017b, Stockholm, Sweden), the microstructures in the 800-1150 • C range contain two different phase zones, i.e., austenite + NbC at 1000-1150 • C and ferrite + NbC at 800-950 • C, which is different from the typical single-austenite-phase deformation condition. In the present study, the two hot-compression-temperature zones (800-950 • C range and 1000-1150 • C range) are discussed and compared with the typical single-temperaturezone condition (800-1150 • C range). In this study, we investigated the hot-deformation behavior of Fe-2 wt% Nb steel by fitting processing parameters and establishing constitutive equations in detail. Based on the above data calculation and model establishment, a hot-processing map was established, which can provide a reliable and accurate strain-processing area, to predict hotdeformation behavior and guide manufacturing and processing.
As shown in Figure 1, which was calculated and drawn using the Thermocalc software (Thermo-Calc 2017b, Stockholm, Sweden), the microstructures in the 800-1150 °C range contain two different phase zones, i.e., austenite + NbC at 1000-1150 °C and ferrite + NbC at 800-950 °C, which is different from the typical single-austenite-phase deformation condition. In the present study, the two hot-compression-temperature zones (800-950 °C range and 1000-1150 °C range) are discussed and compared with the typical singletemperature-zone condition (800-1150 °C range).

Experimental Materials and Procedure
The specific composition of Fe-2 wt% Nb steel is shown in Table 1. A hot-compression experiment was carried out using a Gleeble 3800 thermal simulator (Dynamic Systems Inc., Austin, TX, USA). The sample had a diameter of 8 mm and length of 12 mm. The detailed procedures of the heat treatment and isothermal compressive experiment are shown in Figure 2. The direction of the compression load was perpendicular to the circular surface of the sample.

Experimental Materials and Procedure
The specific composition of Fe-2 wt% Nb steel is shown in Table 1. A hot-compression experiment was carried out using a Gleeble 3800 thermal simulator (Dynamic Systems Inc., Austin, TX, USA). The sample had a diameter of 8 mm and length of 12 mm. The detailed procedures of the heat treatment and isothermal compressive experiment are shown in Figure 2. The direction of the compression load was perpendicular to the circular surface of the sample. The surfaces were mechanically polished and etched with 5 vol.% nital solution for metallographic observation using a light optical microscope (Zeiss, Jena, Germany).

Hot-Compressive Stress-Strain Curves
The true stress-strain curves are shown in Figures 3 and 4. In the early deformation stage, work hardening dominates, which represents a rapid stress increase for the continuous deformation. The surfaces were mechanically polished and etched with 5 vol.% nital solution for metallographic observation using a light optical microscope (Zeiss, Jena, Germany).

Hot-Compressive Stress-Strain Curves
The true stress-strain curves are shown in Figures 3 and 4. In the early deformation stage, work hardening dominates, which represents a rapid stress increase for the continuous deformation. The surfaces were mechanically polished and etched with 5 vol.% nital solution for metallographic observation using a light optical microscope (Zeiss, Jena, Germany).

Hot-Compressive Stress-Strain Curves
The true stress-strain curves are shown in Figures 3 and 4. In the early deformation stage, work hardening dominates, which represents a rapid stress increase for the continuous deformation.    After the work-hardening stage, most of the curves reach a steady state, especially when the materials were deformed at too-low temperatures with high strain rates, indicating that dynamic recovery (DRV) dominated the deformation, as seen in Figure 3d [10]. Only a very small number of curves have obvious stress-softening stages, indicating that dynamic recrystallization (DRX) dominated the deformation, such as at 900 °C and 950 °C with 0.01 s −1 in Figure 3 and 1150 °C with strain rates of 0.01 s −1 and 0.1 s −1 in Figure 4.

Hot-Compressive-Deformation Model
The relationship between the flow stress, σ; strain rate, ε ; and temperature, T, is widely described by an Arrhenius-type hyperbolic-sine relationship and Zener-Hollomon parameter, Z, which can be represented as follows [18,19]: where Q (kJ/mol) is the activation energy; R is the universal gas constant, 8.314 J·mol −1 ·K −1 ; represents the strain rate; A0, A1, and A are structural factors; denotes the stress level parameter; and is a constant. n0 and n are stress exponents. Equations (1) and (3) are applicable to low stress levels, < 0.8; high stress levels, > 1.2; and all stress levels, respectively. After the work-hardening stage, most of the curves reach a steady state, especially when the materials were deformed at too-low temperatures with high strain rates, indicating that dynamic recovery (DRV) dominated the deformation, as seen in Figure 3d [10]. Only a very small number of curves have obvious stress-softening stages, indicating that dynamic recrystallization (DRX) dominated the deformation, such as at 900 • C and 950 • C with 0.01 s −1 in Figure 3 and 1150 • C with strain rates of 0.01 s −1 and 0.1 s −1 in Figure 4.

Hot-Compressive-Deformation Model
The relationship between the flow stress, σ; strain rate, . ε; and temperature, T, is widely described by an Arrhenius-type hyperbolic-sine relationship and Zener-Hollomon parameter, Z, which can be represented as follows [18,19]: where Q (kJ/mol) is the activation energy; R is the universal gas constant, 8.314 J·mol −1 ·K −1 ; . ε represents the strain rate; A 0 , A 1 , and A are structural factors; α denotes the stress level parameter; and β is a constant. n 0 and n are stress exponents. Equations (1) and (3) are applicable to low stress levels, ασ < 0.8; high stress levels, ασ > 1.2; and all stress levels, respectively. As shown in Figure 5, σ versus ln . ε and ln σ versus ln . ε at 800-1150 • C were, respectively, calculated using Equations (1) and (2), complying with the following Equations (4) and (5), and α can be calculated using Equation (6): Metals 2021, 11, x FOR PEER REVIEW 5 of 12 As shown in Figure 5, σ versus lnε and lnσ versus lnε at 800-1150 °C were, respectively, calculated using Equations (1) and (2), complying with the following Equations (4) and (5), and α can be calculated using Equation (6) The stress exponent, n, and the activation energy, Q, can be calculated using Equation  Figure 6, and the correlation coefficients are close to 1.
To further take the log function and deduce the equivalence relation on both sides of Equation (3), the parameters A can be derived, as shown in Figure 7.
Based on the above experimental data, the n0, β, α, n, A, and Q for Fe-2 wt% Nb steel are listed in Table 2. The activation energies of the ferrite + NbC region and austenite + NbC region were separately calculated using two linear ranges, as shown in Figure 6c,d. They were 197.23 kJ/mol and 213.86 kJ/mol, respectively, which are higher than that of a low-carbon AISI1010 steel (177 kJ/mol) [20], and comparable to that of Fe-2Mn-0.3Si-0.1Nb (wt%), which is 280 kJ/mol [21]. This means that the NbC precipitates and solute Nb have effects on the deformation process. Consequently, the constitutive equations can be established as: for the ferrite + NbC dual-phase region, and: for the austenite +NbC dual-phase region.  To further take the log function and deduce the equivalence relation on both sides of Equation (3), the parameters A can be derived, as shown in Figure 7.   As shown in Table 2, most of the parameters obtained in the two temperature ranges are very close; thus, parameters in single temperature range (800-1150 °C) were also calculated with same methods and are listed in Table 2. However, it is shown that most of Based on the above experimental data, the n0, β, α, n, A, and Q for Fe-2 wt% Nb steel are listed in Table 2. The activation energies of the ferrite + NbC region and austenite + NbC region were separately calculated using two linear ranges, as shown in Figure 6c,d. They were 197.23 kJ/mol and 213.86 kJ/mol, respectively, which are higher than that of a lowcarbon AISI1010 steel (177 kJ/mol) [20], and comparable to that of Fe-2Mn-0.3Si-0.1Nb (wt%), which is 280 kJ/mol [21]. This means that the NbC precipitates and solute Nb have effects on the deformation process. Consequently, the constitutive equations can be established as: for the austenite + NbC dual-phase region. As shown in Table 2, most of the parameters obtained in the two temperature ranges are very close; thus, parameters in single temperature range (800-1150 • C) were also calculated with same methods and are listed in Table 2. However, it is shown that most of the parameters were largely different from their counterparts, indicating that separately measuring two temperature regions is much more applicable to our conditions.

Hot-Processing Maps
According to the calculation formula for the hot-processing map [22][23][24], the total power, P, consists of two parts; one is the power consumption, G, and the other is the dissipation of quantity, J, related to the dissipation energy arising from the microstructural changes. The relationship among P, G, and J can be described by Equation (9): The parameter m can be calculated from Equation (10). The power-dissipation efficiency, η, and instability criteria efficiency, ξ . ε , can be calculated using Equations (11) and (12), respectively: m = ∂J/∂G = ∂(ln σ)/∂ ln . ε (10) At a certain strain, the hot-working diagram can be obtained by the superposition of the power-dissipation-efficiency diagram and instability diagram. Figure 8 exhibits the hot-processing maps of 2Nb steel at different strains. The value on the contour line in Figure 8 is the power-dissipation factor, η, which represents the power dissipation required by the evolution of the microstructure in the thermal-deformation system. The larger the η value is, the more likely dynamic recovery and dynamic recrystallization will occur in this region, thus ensuring the reduction of internal defects in the metal and the refinement of the grains. However, not all regions with large η values can obtain products with ideal mechanical properties. When the hot-working parameters meet Equation (12), these regions will have microstructural instability, such as coarse grains or rheological characteristics, so these regions are the instable domains. Thus, Equation (12) is the boundary of the instable and the safe domains.

Microstructural Evolution
To investigate microstructural evolution correlating with stress-strain behavior, the microstructures of specimens after hot compression were characterized by optical microscopy.
As shown in Figure 9a-c, the instability domain with an η of 0.1-0.22 in the temperature range of 800-950 °C with strain rates of 0.03-10 s −1 for a true strain of 0.69 was characterized by mainly elongated grains and a small fraction of recrystallization grains; see the regions indicated by black arrows. This is consistent with previous reports on flow instability resulting in localized plastic flow or cracking [25]. The safe domain with a high power-dissipation efficiency, η, was mainly composed of two stable regions, i.e., the region in a temperature range of 900-950 °C with strain rates of 0.3-10 s −1 and the region in a temperature range of 800-950 °C with strain rates of 0.01-0.2 s −1 , as seen from Figure  9f,i,h. In these domains, η was calculated to be from 0.22 to 0.50, representing a homoge- For the ferrite + NbC dual-phase region, it can be observed that, as the total deformation strain increased, the instable domains covered by shadow gradually diffused from a low-temperature and high-strain-rate region to a high-temperature and low-strain-rate region, and the area of the instable domains gradually increased. The safe domains without shadow for hot processing were located in the region with low strain rates (0.01 s −1 ) at all temperatures, as well as a high strain rate (1-10 s −1 ) at temperatures of about 840-950 • C. The maximum power-dissipation efficiency was 0.5, obtained at 950 • C with 0.01 s −1 , where the optimum processing performance could be obtained. For the austenite + NbC phase region, it can also be seen that the instable domains gradually diffused from a high-strain-rate region to low-strain-rate region with increasing total deformation strain, and the safe domains dwelt approximately in the region from 0.01 s −1 to 0.1 s −1 strain rates at all temperature ranges. The maximum power-dissipation efficiency reached 0.43 at 1000 • C with 0.01 s −1 , where the best processing performance could be achieved.

Microstructural Evolution
To investigate microstructural evolution correlating with stress-strain behavior, the microstructures of specimens after hot compression were characterized by optical microscopy.
As shown in Figure 9a-c, the instability domain with an η of 0.1-0.22 in the temperature range of 800-950 • C with strain rates of 0.03-10 s −1 for a true strain of 0.69 was characterized by mainly elongated grains and a small fraction of recrystallization grains; see the regions indicated by black arrows. This is consistent with previous reports on flow instability resulting in localized plastic flow or cracking [25]. The safe domain with a high power-dissipation efficiency, η, was mainly composed of two stable regions, i.e., the region in a temperature range of 900-950 • C with strain rates of 0.3-10 s −1 and the region in a temperature range of 800-950 • C with strain rates of 0.01-0.2 s −1 , as seen from Figure 9f,h,i. In these domains, η was calculated to be from 0.22 to 0.50, representing a homogeneous and completed recrystallization microstructure. Moreover, it could be found that the grain size decreased with an increase in η, which indicates that sufficient recrystallization requires more energy consumption [26]. Therefore, based on Equations (11) and (12) as well as the validation of optical micrographs, the processing performances of these regions were suitable for actual production. Furthermore, the third microstructural domain was the boundary between the stable region and unstable region, as seen from Figure 9d,g. It could be notably observed that a greatly inhomogeneous microstructure existed from location to location, such as a deformed microstructure in the upper part of Figure 9g and recrystallized microstructure in the lower part of Figure 9g. Therefore, these processing areas should also be avoided in actual production.
Compared with the microstructures for 800-950 • C consisting of a ferrite + NbC phase, the microstructures for 1000-1150 • C composed of austenite + NbC were different, as seen in Figure 10a-i. In the unstable domain with an η of 0.1-0.27 in the temperature range of 1000-1150 • C with strain rates of 0.06-10 s −1 , the grains were relatively coarse, as shown in Figure 10a-c. In addition, further observation shows that, with an increase in the η value, the formation of new grains occurred gradually. As seen in Figure 10f,h,i, it is evident that, in the safe domain, the grains were relatively fine and uniformly distributed, accompanying signs of dynamic recrystallization, where the η varied from 0.31 to 0.43 with strain rates of 0.01-0.36 s −1 in a temperature range of 1000-1150 • C. Compared with the stable domain of 800-950 • C, the grain size was smaller, and the grain boundary morphology was more curved in the stable domain at 1000-1150 • C. In the same way, the grain size decreased with a rise in the η value. As shown in Figure 10d,g, at the boundary between the stable and unstable regions, small grains were embedded by coarse grains, which is slightly different from that at 800-950 • C.
uted, accompanying signs of dynamic recrystallization, where the η varied from 0.31 to 0.43 with strain rates of 0.01-0.36 s −1 in a temperature range of 1000-1150 °C. Compared with the stable domain of 800-950 °C, the grain size was smaller, and the grain boundary morphology was more curved in the stable domain at 1000-1150 °C. In the same way, the grain size decreased with a rise in the η value. As shown in Figure 10d,g, at the boundary between the stable and unstable regions, small grains were embedded by coarse grains, which is slightly different from that at 800-950 °C.

Conclusions
The hot-deformation behavior and microstructural evolution of Fe-2 wt% Nb steel were studied. The Arrhenius constitutive equation together with a microstructural evolution characterization was employed to describe the flow behavior. The relevant conclusions are as follows: for the fcc phase microstructure.
2. Based on the experimental data, the processing maps were obtained. For the ferrite matrix condition, the feasible regions are in the 850-950 °C range with strain rates of 0.4-10 s −1 and 800-950 °C with strain rates of 0.01-0.03 s −1 , respectively. For the austenite matrix, the feasible region ranges from 1000 °C to 1150 °C with strain rates of 0.01-0.05 s −1 .

Conclusions
The hot-deformation behavior and microstructural evolution of Fe-2 wt% Nb steel were studied. The Arrhenius constitutive equation together with a microstructural evolution characterization was employed to describe the flow behavior. The relevant conclusions are as follows: for the fcc phase microstructure.

2.
Based on the experimental data, the processing maps were obtained. For the ferrite matrix condition, the feasible regions are in the 850-950 • C range with strain rates of 0.4-10 s −1 and 800-950 • C with strain rates of 0.01-0.03 s −1 , respectively. For the austenite matrix, the feasible region ranges from 1000 • C to 1150 • C with strain rates of 0.01-0.05 s −1 .

3.
In the safe domains, with an increase in η, the grains are gradually refined, showing a typical recrystallization structure. However, in the instable domains, the grains are elongated and separated without recrystallization, showing typical rheologicalinstability characteristics.

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