# Dynamic Recrystallization and Recovery Behaviors in Austenite of a Novel Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultrahigh Strength Steel

Authors: Yongli Chen; Yuhua Li; Xuejiao Zhou; Yueyue Jiang; Fei Tan
Journal: Journal of Chemistry
 (2021)

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## Abstract

Due to the complex composition and high proportion of alloys in traditional ultrahigh strength steel, the dilemma caused by ultrahigh strength and low toughness in casting and forging processes requiring subsequent heat treatment can be mitigated with an efficient and economical rolling process. In this work, the effect of deformation parameters on dynamic recrystallization (DRX) and dynamic recovery (DRV) is discussed through stress-strain analysis, the DRV mathematical model is obtained, and then the dynamic recrystallization activation energy, Zener–Hollomon equation, and hot working equation are obtained. The critical strain of DRX detected by the P-J method isεc/εp=0.631, which indicates that dynamic recrystallization of this novel steel is relatively easy to achieve by the rolling process. These models and conclusions have potential to be generalized for the formulation of process specification and process configuration without requiring extensive material testing.


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## Body

## 1. Introduction

Ultrahigh strength steel (UHSS) can reduce steel consumption and improve the safety coefficient so significantly that it is widely used in various industrial fields. However, traditional UHSS is difficult to be smelted as a result of a high alloying addition and a complex composition [1]. Accordingly, the strength of the UHSS is sometimes challenging to match its toughness [2–4]. Eventually, steels exhibit high strength but low toughness. New economic and efficient technology is urgently needed to develop to produce UHSS.Physical metallurgical behaviors such as work hardening, dynamic restoration, and dynamic recrystallization compete in development during the austenite hot deformation of UHSS, which determines the rheological stress. Rheological stress can reflect the characteristic of UHSS dynamic recrystallization (DRX) [5]. In rolling process, DRX curve can be obtained by three different mechanisms: discontinuous dynamic recrystallization (DDRX), continuous dynamic recrystallization (CDRX), and geometric dynamic recrystallization (GDRX) [6, 7]. The stacking fault energy of UHSS attributed to Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo steel is relatively complex, which can be estimated qualitatively from the deformation of work hardening in the flow stress curves [8]. Much attention has been paid to calculate the deformation of carbon steels and austenitic stainless steel [9–11]. Besides, Haridas et al. [12] and Chen et al. [13] studied hot compression effects of deformation temperature, strain rate, and the strain on the microstructural evolution. Zhu et al. [14] investigated the influence of high-temperature deformation and heat treatment on the microstructure of AF1410 in a high Co-Ni aging secondary hardening UHSS. Chen et al. [15] simulated the recrystallization of forging 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation. But little attention has been paid to the high stacking fault energy of the UHSS flow behaviors, which aimed at the efficient direct hot rolling production process.According to the difference of strain hardening behaviors between DRV and DRX, Ryan and McQueen [16, 17] defined εc as the critical strain where θ and σ begin to deviate from the linear relationship in the θ-σ curve based on the relationship between strain hardening rate θ=θ=dσ/dε and true stress σ, which is called R-M method. Poliak and Jonas et al. [5, 18–20] defined the critical stress σc as the stress at the point of −∂θ/∂σmin on the −−∂θ/∂σ−σ (θ is the strain hardening rate) and determined σc and εc directly from the stress-strain curve by the P-J method.This work focuses on the exploitation of a novel bainitic Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo UHSS by a compact hot rolling process. A thermodynamic simulation experiment for the hot rolling process of experimental steel was carried out to analyze and establish the constitutive equation and dynamic recrystallization model of austenite subjected to the hot deformation. According to P-J method, the critical strain for dynamic recrystallization of austenite was determined, and then the variation law of critical strain under different deformation conditions was studied. Dynamic recrystallization behaviors and austenite refinement were investigated in detail. The theoretical basis and practical guidance for the rolling process of UHSS are provided, which can be expected to have both fundamental and practical significance. We offer an alternative scheme to develop a more economic and efficient process for the UHSS production.


## 2. Experimental Materials and Procedures

### 2.1. Experimental Materials

Experimental steel was smelted in a 150 kg vacuum induction furnace. Harmful elements of testing steel, such as S and P, were strictly controlled. The chemical compositions (wt.%) of experimental samples were 0.23C, 1.95Si, 1.93 Mn, 0.007P, 0.003S, 0.07Ni, 1.96Cr, 0.35Mo, and Nb + V + Ti ≤2.0. It was rolled into 10 mm thick steel sheet byϕ 450 hot rolling mills. The finished sheet was air-cooled. Then the specimens were cut horizontally at a quarter width position of the sheet and etched by 4% (Vol.%) nitric acid alcohol for metallography after being ground and polished. LEICA 2500M (Leica, Wetzlar, Germany) was applied to observe the microstructure of the examined steel. Tensile tests were performed in a WAW-1000 (SUST Electric Equipment Co., Ltd., Zhuhai, China) to determine the engineering stress.


### 2.2. Experimental Procedures

The above hot rolled and air-cooled sheet was prepared forϕ 8 mm × 15 mm thermal simulation samples, and then the experiments were carried out on MMS-300 thermal simulator (RAL of Northeastern University, Shenyang, China). The schematic illustration of single-pass compression experiment is shown in Figure 1. The sample, whose both ends were stained with graphite to reduce friction and avoid the adhesion to achieving homogeneous compression deformation, was heated to 1200°C at a heating rate of 10°C·s−1 and kept for 180 s at 1200°C to reach a fully austenitized state for the internal structure, and then it was cooled at cooling rate of 10°C·s−1 to the different temperature of 850°C, 900°C, 950°C, 1000°C, and 1050°C, respectively. After holding for 20 s to eliminate the internal temperature gradient, the tested sample was compressed with true strain of 1 at different strain rates of 0.01 s−1, 0.1 s−1, 0.5 s−1, 1 s−1, and 5 s−1, respectively. The hot deformed temperature of 850–1050°C is ordinary for direct hot rolling (1250–950°C) and controlled hot rolling (above 850°C). The strain rate is 0.01–0.5 s−1, which mainly simulates typical hot rolling for the medium sheets rolling (slow rolling rate), hot bar rolling (medium rolling rate), and high speed wire rolling (high rolling rate) in the hot rolling process in the factory. The true strain is 1; that is to say, the engineering strain is 63%, which mainly simulates typical high temperature and large reduction deformation in the steel rolling process. Then the effects of deformation parameters such as deformation temperature, deformation rate, and deformation strain on the stress were discussed.Figure 1
Schematic illustration of single-pass compression experiment.


### 2.3. Microstructural Characterization

Single-pass compressed specimens were cut along the compression axis by wire spark cutting machine. Afterward, they were etched with saturated picric acid alcohol solution with 2 vol.% Haiou shampoo and 2 wt.% sodium benzene sulfonate aqueous at room temperature for the characterization of austenite grain boundaries after being ground and polished. Then the morphology of samples was obtained by Leica-DM 2500M (Leica, Wetzlar, Germany) light microscope.


## 2.1. Experimental Materials

Experimental steel was smelted in a 150 kg vacuum induction furnace. Harmful elements of testing steel, such as S and P, were strictly controlled. The chemical compositions (wt.%) of experimental samples were 0.23C, 1.95Si, 1.93 Mn, 0.007P, 0.003S, 0.07Ni, 1.96Cr, 0.35Mo, and Nb + V + Ti ≤2.0. It was rolled into 10 mm thick steel sheet byϕ 450 hot rolling mills. The finished sheet was air-cooled. Then the specimens were cut horizontally at a quarter width position of the sheet and etched by 4% (Vol.%) nitric acid alcohol for metallography after being ground and polished. LEICA 2500M (Leica, Wetzlar, Germany) was applied to observe the microstructure of the examined steel. Tensile tests were performed in a WAW-1000 (SUST Electric Equipment Co., Ltd., Zhuhai, China) to determine the engineering stress.


## 2.2. Experimental Procedures

The above hot rolled and air-cooled sheet was prepared forϕ 8 mm × 15 mm thermal simulation samples, and then the experiments were carried out on MMS-300 thermal simulator (RAL of Northeastern University, Shenyang, China). The schematic illustration of single-pass compression experiment is shown in Figure 1. The sample, whose both ends were stained with graphite to reduce friction and avoid the adhesion to achieving homogeneous compression deformation, was heated to 1200°C at a heating rate of 10°C·s−1 and kept for 180 s at 1200°C to reach a fully austenitized state for the internal structure, and then it was cooled at cooling rate of 10°C·s−1 to the different temperature of 850°C, 900°C, 950°C, 1000°C, and 1050°C, respectively. After holding for 20 s to eliminate the internal temperature gradient, the tested sample was compressed with true strain of 1 at different strain rates of 0.01 s−1, 0.1 s−1, 0.5 s−1, 1 s−1, and 5 s−1, respectively. The hot deformed temperature of 850–1050°C is ordinary for direct hot rolling (1250–950°C) and controlled hot rolling (above 850°C). The strain rate is 0.01–0.5 s−1, which mainly simulates typical hot rolling for the medium sheets rolling (slow rolling rate), hot bar rolling (medium rolling rate), and high speed wire rolling (high rolling rate) in the hot rolling process in the factory. The true strain is 1; that is to say, the engineering strain is 63%, which mainly simulates typical high temperature and large reduction deformation in the steel rolling process. Then the effects of deformation parameters such as deformation temperature, deformation rate, and deformation strain on the stress were discussed.Figure 1
Schematic illustration of single-pass compression experiment.


## 2.3. Microstructural Characterization

Single-pass compressed specimens were cut along the compression axis by wire spark cutting machine. Afterward, they were etched with saturated picric acid alcohol solution with 2 vol.% Haiou shampoo and 2 wt.% sodium benzene sulfonate aqueous at room temperature for the characterization of austenite grain boundaries after being ground and polished. Then the morphology of samples was obtained by Leica-DM 2500M (Leica, Wetzlar, Germany) light microscope.


## 3. Results and Discussion

### 3.1. Original Microstructures and Mechanical Properties

The original microstructure of the examined steel and the results indicated that it is mainly composed of martensite (M) and bainite (B), as shown in Figure2(a). The mechanical properties of tensile and hardness are presented in Figure 2(b), which shows that yield strength (YS), tensile strength (TS), and elongation (A), are 1260 MPa, 1570 MPa, and 16%, respectively. Thus, the excellent combination of strength and toughness indicates that the rolled UHSS had excellent performance. Therefore, this work offered technical and theoretical support for the rolling production of such extraordinary strength-toughness steel.Figure 2
Original microstructure (a) and mechanical properties (b) of examined steel.
(a)(b)


### 3.2. Flow Characteristics and Deformation Mechanisms

#### 3.2.1. Effect of Strain Rate on Dynamic Recrystallization

Figure3 shows the true stress-true strain curves without friction correction for the experimental steels at 850°C and 1050°C. With a strain rate of 0.01 s−1 at 850°C, the stress-strain curve is a typical pattern of the steel DRX. When the stress increases to the peak stress, it is meaningful to find that the stress does not increase with the strain, but DRX can still be observed. When the strain rate is increased above 0.1 s−1, the austenite exhibits properties of DRV and work hardening during hot working. It indicates that the strain rate of 0.1 s−1 presents a distinct DRX characteristic at 1050°C in the austenite zone.Figure 3
Influences of strain rates on flow stress at 850°C (a) and 1050°C (b).
(a)(b)Comparative analysis of Figures3(a) and 3(b) shows that DRX of the tested materials is difficult to happen at a relatively high deformation rate. Nevertheless, it is worthy to note that DRX occurs again when the temperature increased to 1050°C from 850°C. This phenomenon indicated that the lower the strain rate is, the lower εp and εc of the true stress-true strain curve are, and the DRX is easy to occur at the same deformation temperature. Wang et al. [21] also found that the true stress decreases with the reduced strain rate or the raised temperature. Ansari et al. [22] developed a dislocation-based constitutive model associated with DRV and clarified work hardening mechanisms. As can be seen from Figure 3(b), the true stress-true strain curve can well reflect DRX characteristics at the strain rate of 0.01–0.1 s−1. Further increase of strain rate is conducive to increase εp and εc, while DRX is difficult to occur. When the strain increased to 0.5 s−1, the flow stress reaches σp and then keeps a stable flow state. When the deformation was implemented at a lower temperature and higher strain rate, the increase of ε could result in the distortion to the lattice of internal grains under the action of external pressure, and DRX did not occur in time for the hardening austenite. At this condition, the stress-strain curve was DRV-shaped.


#### 3.2.2. Effect of Deformation Temperature on Dynamic Recrystallization

Figure4 displays the true stress-strain curves without friction correction at deformation rates of 0.01 s−1 and 5 s−1. Under the same strain deformation and the strain rate of 0.01 s−1 in Figure 4(a), it is easy to find that the increase of temperature creates slip condition for plastic deformations, and it is also beneficial to decrease the internal resistance of deformation accordingly. Consequently, the deformation resistance is a result of multifactor competition, and deformation temperature is one of the most significant factors. Figure 4(b) indicates that DRX was challenging to occur at a high strain rate. Raising the deformation rate and decreasing the deformation temperature are detrimental to the occurrence of DRX. DRX is more likely to occur at a low strain rate. At the same time, the true stress again increases with the further increase of strain when the deformation degree is relatively large, as shown in Figures 3 and 4. This phenomenon is because as the deformation increases, the new austenite grains’ internal dislocations increase significantly, showing an early stage of work hardening characteristics.Figure 4
Influences of temperatures on flow stress at strain rates 0.01 s−1 (a) and 0.5 s−1 (b).
(a)(b)Figure5(a) is the undeformed metallography and Figures 5(b)–5(d) are the experimental steel at a high temperature of 1050°C with the strain rate of 0.5 s−1, 0.1 s−1, and 0.01 s−1, respectively. The austenite of undeformed in Figure 5(a) presents a polygonal morphology. From Figure 5(b), the austenite presents a severely flat morphology, but obvious recrystallization is not observed due to DRV. When the strain rate is 0.1 s−1, the hardened austenite is experienced the continuously recrystallizes, the newly formed austenite nucleates along the original grain boundaries, and it presents a deformation and partial recrystallization. As the strain rate is further reduced to 0.01 s−1, the number of recrystallized grains increases significantly. It indicates that austenite DRX transforms decrease with the increase of strain rate. At the same time, it shows that the grains of newly formed austenite in Figures 5(c) and 5(d) are smaller than the original austenite in Figure 5(a). However, as the deformation increases, the newly formed austenite grains are squashed again, but a new dynamic recrystallization is not initiated, and a mass of dislocations and subgrains is generated, resulting in the stress increases again with the further increase of strain in Figures 3 and 4.Figure 5
Austenite grain metallography of undeformed (a) strain rate 0.5 s−1 at 1050°C, (b) strain rate 0.1 s−1 at 1050°C, and (c) strain rate 0.01 s−1 at 1050°C.
(a)(b)(c)(d)


### 3.3. Dynamic Recrystallization Model and Critical Strain

Under isothermal deformation condition of a higher stress state, the stress-strain curve can be calculated according to the strain rate and deformation temperature by the Zener–Hollomon parameter equation of the temperature compensation strain rate. For theZ-parameter model equation of dynamic recrystallization, different scholars proposed different parameter corrections and derivation methods [23–25] and obtained a variety of expressions for the model equations. Through systematic analysis and research, the dynamic recrystallization model can be described as (1)Z=ε˙expQdRT=Asinhασpn,where ε˙ is the strain rate, s−1; Qd is the activation energy of DRX, J·mol−1; T is the absolute temperature of deformation, K; R is the gas constant, J·mol−1·K−1; A is the structural factor of the model, s−1; α is material stress level parameters, MPa−1; σp is the peak stress of the true stress-true strain curve, MPa; and n is the stress exponent of the model.Because the flow stress is dynamic recovery type at lower temperature and higher strain rate, it is appropriate and accurate to analyze the DRX at high temperature by using the experimental data of 950, 1000, and 1050°C.


#### 3.3.1. Dynamic Recrystallization Model

TheZ-parameter determines the stress-strain curve. Sellars et al. [26] proposed a universally applicable hyperbolic sine relation between ε˙, T, and σ under isothermal deformation as follows:(2)Asinhασpn=ε˙expQdRT=Z,(3)ε˙=Asinhασpnexp−QdRT.Kai and Koop [27] suggested that (3) could be simplified to the following model:(4)ε˙=A2σpn′exp−QdRT.Equation (4) can be simplified by taking the natural logarithm:(5)lnσp=1n′lnε˙−1n′lnA2+Qdn′RT.According to (5), there is a linear relationship between ln σpvs.lnε˙ and ln σpvs. 1/T, as shown in Figure 6. It can be deduced that n′=∂lnε˙/lnσpT, b=∂lnsinhασp/∂1/T, Qd=n′Rb. The values of n′ in Figure 6(a) and b in Figure 6(b) obtained by regression are shown in Tables 1 and 2. The average value of n′ is 6.9798, and the average value of b is 8689.6991.Figure 6
Plots of lnσp vs. lnε˙ (a) and ln σp vs. 1/T (b).
(a)(b)Table 1
The value ofn′ fitted at different strain rates and temperatures.
Fitted parameter950°C1000°C1050°Cn′8.92516.81285.2015R20.95270.97380.9621Table 2
The value ofb fitted at different strain rates and temperatures.
Fitted parameter0.01 s−10.01 s−10.01 s−10.01 s−10.01 s−1b13675.644611260.35226059.02634974.73297478.7393R20.99990.906220.85010.87150.9824According to the values ofn′ and b, the activation energy of DRX can be calculated as follows: Qd=8.314×6.9798×8689.6991J·mol−1≈504264J·mol−1.By substituting the DRX activation energyQd into (1), the Z-parameter model is obtained as follows:(6)Z=ε˙exp504264RT.The value ofA2 can be determined by (6) and (1). At different strain rates and temperatures, the average value of A2 is 0.6089 s−1. Substituting the calculated A2 into (1), then the hot working equation can be described as follows:(7)ε˙=0.6089σp6.9798exp−504264RT.The peak flow stressσp is expressed as(8)σp=10.6089ε˙exp504264RT−6.9798.


#### 3.3.2. Critical Strain of Dynamic Recrystallization

The P-J method is more accurate in determining the critical conditions of DRX. A typical (−∂θ/∂σ)-σ curve for UHSS is shown in Figure 7. The flow stress corresponding to the minimum value on the curve is σc of the DRX process, and the strain corresponding to σc on the true stress-true strain curve is εc of the DRX critical strain.Figure 7
Plots of−∂θ/∂σ and σ.The ratioεc/εp reflects the relationship between softening and work hardening in the DRX process. If the softening ability of DRX is significant or the work hardening ability is small, the ratio εc/εp is larger. On the contrary, εc/εp is lower if the softening capacity of DRX is small or the work hardening ability is significant. The average εc/εp of DRX is 0.631 by calculation. It is close to the lower limit of empirical formula εc≈0.60−0.85εp, which indicates that DRX is relatively easy to occur in UHSS under the condition of high temperature and low strain rate.


#### 3.3.3. Relationship between Critical Strain andZ-Parameters

The determination of the critical strainεc at the beginning of DRX during hot deformation is of considerable significance to the study of the hot deformation process and the formulation of a reduction schedule. Because A2σpn′ is equal to Z, the relationship between parameter Z and peak strain εp and critical strain εc can be described as (9)εp=0.045lnZ−0.899,(10)εc=0.028lnZ−0.567.As can be seen from Figure8, the empirical formula between ln Z and σp can be calculated. The relationship between the peak strain εp corresponding to the peak stress σp and the dynamic recrystallization critical strain is εc≈0.60−0.85εp. Thus, (10) of the critical strain εc and ln Z of DRX can be further obtained. Consequently, the peak strain εp and the critical strain εc are linear with ln Z, and the value of parameter Z decreases. Then the peak strain εp decreases and the critical deformation εc of DRX reduces, which indicates that DRX is easy to occur.Figure 8
Plot ofεp versus ln Z.


## 3.1. Original Microstructures and Mechanical Properties

The original microstructure of the examined steel and the results indicated that it is mainly composed of martensite (M) and bainite (B), as shown in Figure2(a). The mechanical properties of tensile and hardness are presented in Figure 2(b), which shows that yield strength (YS), tensile strength (TS), and elongation (A), are 1260 MPa, 1570 MPa, and 16%, respectively. Thus, the excellent combination of strength and toughness indicates that the rolled UHSS had excellent performance. Therefore, this work offered technical and theoretical support for the rolling production of such extraordinary strength-toughness steel.Figure 2
Original microstructure (a) and mechanical properties (b) of examined steel.
(a)(b)


## 3.2. Flow Characteristics and Deformation Mechanisms

### 3.2.1. Effect of Strain Rate on Dynamic Recrystallization

Figure3 shows the true stress-true strain curves without friction correction for the experimental steels at 850°C and 1050°C. With a strain rate of 0.01 s−1 at 850°C, the stress-strain curve is a typical pattern of the steel DRX. When the stress increases to the peak stress, it is meaningful to find that the stress does not increase with the strain, but DRX can still be observed. When the strain rate is increased above 0.1 s−1, the austenite exhibits properties of DRV and work hardening during hot working. It indicates that the strain rate of 0.1 s−1 presents a distinct DRX characteristic at 1050°C in the austenite zone.Figure 3
Influences of strain rates on flow stress at 850°C (a) and 1050°C (b).
(a)(b)Comparative analysis of Figures3(a) and 3(b) shows that DRX of the tested materials is difficult to happen at a relatively high deformation rate. Nevertheless, it is worthy to note that DRX occurs again when the temperature increased to 1050°C from 850°C. This phenomenon indicated that the lower the strain rate is, the lower εp and εc of the true stress-true strain curve are, and the DRX is easy to occur at the same deformation temperature. Wang et al. [21] also found that the true stress decreases with the reduced strain rate or the raised temperature. Ansari et al. [22] developed a dislocation-based constitutive model associated with DRV and clarified work hardening mechanisms. As can be seen from Figure 3(b), the true stress-true strain curve can well reflect DRX characteristics at the strain rate of 0.01–0.1 s−1. Further increase of strain rate is conducive to increase εp and εc, while DRX is difficult to occur. When the strain increased to 0.5 s−1, the flow stress reaches σp and then keeps a stable flow state. When the deformation was implemented at a lower temperature and higher strain rate, the increase of ε could result in the distortion to the lattice of internal grains under the action of external pressure, and DRX did not occur in time for the hardening austenite. At this condition, the stress-strain curve was DRV-shaped.


### 3.2.2. Effect of Deformation Temperature on Dynamic Recrystallization

Figure4 displays the true stress-strain curves without friction correction at deformation rates of 0.01 s−1 and 5 s−1. Under the same strain deformation and the strain rate of 0.01 s−1 in Figure 4(a), it is easy to find that the increase of temperature creates slip condition for plastic deformations, and it is also beneficial to decrease the internal resistance of deformation accordingly. Consequently, the deformation resistance is a result of multifactor competition, and deformation temperature is one of the most significant factors. Figure 4(b) indicates that DRX was challenging to occur at a high strain rate. Raising the deformation rate and decreasing the deformation temperature are detrimental to the occurrence of DRX. DRX is more likely to occur at a low strain rate. At the same time, the true stress again increases with the further increase of strain when the deformation degree is relatively large, as shown in Figures 3 and 4. This phenomenon is because as the deformation increases, the new austenite grains’ internal dislocations increase significantly, showing an early stage of work hardening characteristics.Figure 4
Influences of temperatures on flow stress at strain rates 0.01 s−1 (a) and 0.5 s−1 (b).
(a)(b)Figure5(a) is the undeformed metallography and Figures 5(b)–5(d) are the experimental steel at a high temperature of 1050°C with the strain rate of 0.5 s−1, 0.1 s−1, and 0.01 s−1, respectively. The austenite of undeformed in Figure 5(a) presents a polygonal morphology. From Figure 5(b), the austenite presents a severely flat morphology, but obvious recrystallization is not observed due to DRV. When the strain rate is 0.1 s−1, the hardened austenite is experienced the continuously recrystallizes, the newly formed austenite nucleates along the original grain boundaries, and it presents a deformation and partial recrystallization. As the strain rate is further reduced to 0.01 s−1, the number of recrystallized grains increases significantly. It indicates that austenite DRX transforms decrease with the increase of strain rate. At the same time, it shows that the grains of newly formed austenite in Figures 5(c) and 5(d) are smaller than the original austenite in Figure 5(a). However, as the deformation increases, the newly formed austenite grains are squashed again, but a new dynamic recrystallization is not initiated, and a mass of dislocations and subgrains is generated, resulting in the stress increases again with the further increase of strain in Figures 3 and 4.Figure 5
Austenite grain metallography of undeformed (a) strain rate 0.5 s−1 at 1050°C, (b) strain rate 0.1 s−1 at 1050°C, and (c) strain rate 0.01 s−1 at 1050°C.
(a)(b)(c)(d)


## 3.2.1. Effect of Strain Rate on Dynamic Recrystallization

Figure3 shows the true stress-true strain curves without friction correction for the experimental steels at 850°C and 1050°C. With a strain rate of 0.01 s−1 at 850°C, the stress-strain curve is a typical pattern of the steel DRX. When the stress increases to the peak stress, it is meaningful to find that the stress does not increase with the strain, but DRX can still be observed. When the strain rate is increased above 0.1 s−1, the austenite exhibits properties of DRV and work hardening during hot working. It indicates that the strain rate of 0.1 s−1 presents a distinct DRX characteristic at 1050°C in the austenite zone.Figure 3
Influences of strain rates on flow stress at 850°C (a) and 1050°C (b).
(a)(b)Comparative analysis of Figures3(a) and 3(b) shows that DRX of the tested materials is difficult to happen at a relatively high deformation rate. Nevertheless, it is worthy to note that DRX occurs again when the temperature increased to 1050°C from 850°C. This phenomenon indicated that the lower the strain rate is, the lower εp and εc of the true stress-true strain curve are, and the DRX is easy to occur at the same deformation temperature. Wang et al. [21] also found that the true stress decreases with the reduced strain rate or the raised temperature. Ansari et al. [22] developed a dislocation-based constitutive model associated with DRV and clarified work hardening mechanisms. As can be seen from Figure 3(b), the true stress-true strain curve can well reflect DRX characteristics at the strain rate of 0.01–0.1 s−1. Further increase of strain rate is conducive to increase εp and εc, while DRX is difficult to occur. When the strain increased to 0.5 s−1, the flow stress reaches σp and then keeps a stable flow state. When the deformation was implemented at a lower temperature and higher strain rate, the increase of ε could result in the distortion to the lattice of internal grains under the action of external pressure, and DRX did not occur in time for the hardening austenite. At this condition, the stress-strain curve was DRV-shaped.


## 3.2.2. Effect of Deformation Temperature on Dynamic Recrystallization

Figure4 displays the true stress-strain curves without friction correction at deformation rates of 0.01 s−1 and 5 s−1. Under the same strain deformation and the strain rate of 0.01 s−1 in Figure 4(a), it is easy to find that the increase of temperature creates slip condition for plastic deformations, and it is also beneficial to decrease the internal resistance of deformation accordingly. Consequently, the deformation resistance is a result of multifactor competition, and deformation temperature is one of the most significant factors. Figure 4(b) indicates that DRX was challenging to occur at a high strain rate. Raising the deformation rate and decreasing the deformation temperature are detrimental to the occurrence of DRX. DRX is more likely to occur at a low strain rate. At the same time, the true stress again increases with the further increase of strain when the deformation degree is relatively large, as shown in Figures 3 and 4. This phenomenon is because as the deformation increases, the new austenite grains’ internal dislocations increase significantly, showing an early stage of work hardening characteristics.Figure 4
Influences of temperatures on flow stress at strain rates 0.01 s−1 (a) and 0.5 s−1 (b).
(a)(b)Figure5(a) is the undeformed metallography and Figures 5(b)–5(d) are the experimental steel at a high temperature of 1050°C with the strain rate of 0.5 s−1, 0.1 s−1, and 0.01 s−1, respectively. The austenite of undeformed in Figure 5(a) presents a polygonal morphology. From Figure 5(b), the austenite presents a severely flat morphology, but obvious recrystallization is not observed due to DRV. When the strain rate is 0.1 s−1, the hardened austenite is experienced the continuously recrystallizes, the newly formed austenite nucleates along the original grain boundaries, and it presents a deformation and partial recrystallization. As the strain rate is further reduced to 0.01 s−1, the number of recrystallized grains increases significantly. It indicates that austenite DRX transforms decrease with the increase of strain rate. At the same time, it shows that the grains of newly formed austenite in Figures 5(c) and 5(d) are smaller than the original austenite in Figure 5(a). However, as the deformation increases, the newly formed austenite grains are squashed again, but a new dynamic recrystallization is not initiated, and a mass of dislocations and subgrains is generated, resulting in the stress increases again with the further increase of strain in Figures 3 and 4.Figure 5
Austenite grain metallography of undeformed (a) strain rate 0.5 s−1 at 1050°C, (b) strain rate 0.1 s−1 at 1050°C, and (c) strain rate 0.01 s−1 at 1050°C.
(a)(b)(c)(d)


## 3.3. Dynamic Recrystallization Model and Critical Strain

Under isothermal deformation condition of a higher stress state, the stress-strain curve can be calculated according to the strain rate and deformation temperature by the Zener–Hollomon parameter equation of the temperature compensation strain rate. For theZ-parameter model equation of dynamic recrystallization, different scholars proposed different parameter corrections and derivation methods [23–25] and obtained a variety of expressions for the model equations. Through systematic analysis and research, the dynamic recrystallization model can be described as (1)Z=ε˙expQdRT=Asinhασpn,where ε˙ is the strain rate, s−1; Qd is the activation energy of DRX, J·mol−1; T is the absolute temperature of deformation, K; R is the gas constant, J·mol−1·K−1; A is the structural factor of the model, s−1; α is material stress level parameters, MPa−1; σp is the peak stress of the true stress-true strain curve, MPa; and n is the stress exponent of the model.Because the flow stress is dynamic recovery type at lower temperature and higher strain rate, it is appropriate and accurate to analyze the DRX at high temperature by using the experimental data of 950, 1000, and 1050°C.


### 3.3.1. Dynamic Recrystallization Model

TheZ-parameter determines the stress-strain curve. Sellars et al. [26] proposed a universally applicable hyperbolic sine relation between ε˙, T, and σ under isothermal deformation as follows:(2)Asinhασpn=ε˙expQdRT=Z,(3)ε˙=Asinhασpnexp−QdRT.Kai and Koop [27] suggested that (3) could be simplified to the following model:(4)ε˙=A2σpn′exp−QdRT.Equation (4) can be simplified by taking the natural logarithm:(5)lnσp=1n′lnε˙−1n′lnA2+Qdn′RT.According to (5), there is a linear relationship between ln σpvs.lnε˙ and ln σpvs. 1/T, as shown in Figure 6. It can be deduced that n′=∂lnε˙/lnσpT, b=∂lnsinhασp/∂1/T, Qd=n′Rb. The values of n′ in Figure 6(a) and b in Figure 6(b) obtained by regression are shown in Tables 1 and 2. The average value of n′ is 6.9798, and the average value of b is 8689.6991.Figure 6
Plots of lnσp vs. lnε˙ (a) and ln σp vs. 1/T (b).
(a)(b)Table 1
The value ofn′ fitted at different strain rates and temperatures.
Fitted parameter950°C1000°C1050°Cn′8.92516.81285.2015R20.95270.97380.9621Table 2
The value ofb fitted at different strain rates and temperatures.
Fitted parameter0.01 s−10.01 s−10.01 s−10.01 s−10.01 s−1b13675.644611260.35226059.02634974.73297478.7393R20.99990.906220.85010.87150.9824According to the values ofn′ and b, the activation energy of DRX can be calculated as follows: Qd=8.314×6.9798×8689.6991J·mol−1≈504264J·mol−1.By substituting the DRX activation energyQd into (1), the Z-parameter model is obtained as follows:(6)Z=ε˙exp504264RT.The value ofA2 can be determined by (6) and (1). At different strain rates and temperatures, the average value of A2 is 0.6089 s−1. Substituting the calculated A2 into (1), then the hot working equation can be described as follows:(7)ε˙=0.6089σp6.9798exp−504264RT.The peak flow stressσp is expressed as(8)σp=10.6089ε˙exp504264RT−6.9798.


### 3.3.2. Critical Strain of Dynamic Recrystallization

The P-J method is more accurate in determining the critical conditions of DRX. A typical (−∂θ/∂σ)-σ curve for UHSS is shown in Figure 7. The flow stress corresponding to the minimum value on the curve is σc of the DRX process, and the strain corresponding to σc on the true stress-true strain curve is εc of the DRX critical strain.Figure 7
Plots of−∂θ/∂σ and σ.The ratioεc/εp reflects the relationship between softening and work hardening in the DRX process. If the softening ability of DRX is significant or the work hardening ability is small, the ratio εc/εp is larger. On the contrary, εc/εp is lower if the softening capacity of DRX is small or the work hardening ability is significant. The average εc/εp of DRX is 0.631 by calculation. It is close to the lower limit of empirical formula εc≈0.60−0.85εp, which indicates that DRX is relatively easy to occur in UHSS under the condition of high temperature and low strain rate.


### 3.3.3. Relationship between Critical Strain andZ-Parameters

The determination of the critical strainεc at the beginning of DRX during hot deformation is of considerable significance to the study of the hot deformation process and the formulation of a reduction schedule. Because A2σpn′ is equal to Z, the relationship between parameter Z and peak strain εp and critical strain εc can be described as (9)εp=0.045lnZ−0.899,(10)εc=0.028lnZ−0.567.As can be seen from Figure8, the empirical formula between ln Z and σp can be calculated. The relationship between the peak strain εp corresponding to the peak stress σp and the dynamic recrystallization critical strain is εc≈0.60−0.85εp. Thus, (10) of the critical strain εc and ln Z of DRX can be further obtained. Consequently, the peak strain εp and the critical strain εc are linear with ln Z, and the value of parameter Z decreases. Then the peak strain εp decreases and the critical deformation εc of DRX reduces, which indicates that DRX is easy to occur.Figure 8
Plot ofεp versus ln Z.


## 3.3.1. Dynamic Recrystallization Model

TheZ-parameter determines the stress-strain curve. Sellars et al. [26] proposed a universally applicable hyperbolic sine relation between ε˙, T, and σ under isothermal deformation as follows:(2)Asinhασpn=ε˙expQdRT=Z,(3)ε˙=Asinhασpnexp−QdRT.Kai and Koop [27] suggested that (3) could be simplified to the following model:(4)ε˙=A2σpn′exp−QdRT.Equation (4) can be simplified by taking the natural logarithm:(5)lnσp=1n′lnε˙−1n′lnA2+Qdn′RT.According to (5), there is a linear relationship between ln σpvs.lnε˙ and ln σpvs. 1/T, as shown in Figure 6. It can be deduced that n′=∂lnε˙/lnσpT, b=∂lnsinhασp/∂1/T, Qd=n′Rb. The values of n′ in Figure 6(a) and b in Figure 6(b) obtained by regression are shown in Tables 1 and 2. The average value of n′ is 6.9798, and the average value of b is 8689.6991.Figure 6
Plots of lnσp vs. lnε˙ (a) and ln σp vs. 1/T (b).
(a)(b)Table 1
The value ofn′ fitted at different strain rates and temperatures.
Fitted parameter950°C1000°C1050°Cn′8.92516.81285.2015R20.95270.97380.9621Table 2
The value ofb fitted at different strain rates and temperatures.
Fitted parameter0.01 s−10.01 s−10.01 s−10.01 s−10.01 s−1b13675.644611260.35226059.02634974.73297478.7393R20.99990.906220.85010.87150.9824According to the values ofn′ and b, the activation energy of DRX can be calculated as follows: Qd=8.314×6.9798×8689.6991J·mol−1≈504264J·mol−1.By substituting the DRX activation energyQd into (1), the Z-parameter model is obtained as follows:(6)Z=ε˙exp504264RT.The value ofA2 can be determined by (6) and (1). At different strain rates and temperatures, the average value of A2 is 0.6089 s−1. Substituting the calculated A2 into (1), then the hot working equation can be described as follows:(7)ε˙=0.6089σp6.9798exp−504264RT.The peak flow stressσp is expressed as(8)σp=10.6089ε˙exp504264RT−6.9798.


## 3.3.2. Critical Strain of Dynamic Recrystallization

The P-J method is more accurate in determining the critical conditions of DRX. A typical (−∂θ/∂σ)-σ curve for UHSS is shown in Figure 7. The flow stress corresponding to the minimum value on the curve is σc of the DRX process, and the strain corresponding to σc on the true stress-true strain curve is εc of the DRX critical strain.Figure 7
Plots of−∂θ/∂σ and σ.The ratioεc/εp reflects the relationship between softening and work hardening in the DRX process. If the softening ability of DRX is significant or the work hardening ability is small, the ratio εc/εp is larger. On the contrary, εc/εp is lower if the softening capacity of DRX is small or the work hardening ability is significant. The average εc/εp of DRX is 0.631 by calculation. It is close to the lower limit of empirical formula εc≈0.60−0.85εp, which indicates that DRX is relatively easy to occur in UHSS under the condition of high temperature and low strain rate.


## 3.3.3. Relationship between Critical Strain andZ-Parameters

The determination of the critical strainεc at the beginning of DRX during hot deformation is of considerable significance to the study of the hot deformation process and the formulation of a reduction schedule. Because A2σpn′ is equal to Z, the relationship between parameter Z and peak strain εp and critical strain εc can be described as (9)εp=0.045lnZ−0.899,(10)εc=0.028lnZ−0.567.As can be seen from Figure8, the empirical formula between ln Z and σp can be calculated. The relationship between the peak strain εp corresponding to the peak stress σp and the dynamic recrystallization critical strain is εc≈0.60−0.85εp. Thus, (10) of the critical strain εc and ln Z of DRX can be further obtained. Consequently, the peak strain εp and the critical strain εc are linear with ln Z, and the value of parameter Z decreases. Then the peak strain εp decreases and the critical deformation εc of DRX reduces, which indicates that DRX is easy to occur.Figure 8
Plot ofεp versus ln Z.


## 4. Conclusions

This paper has studied the influences of deformation parameters on DRX and DRV by stress-strain, and the DRX model has been constructed. The main achievements are summarized as follows:(1)
Dynamic recrystallization and recovery behaviors are obviously affected by deformation temperature and strain rate. The flow stress drops with the reduced strain rate or the raised deformation temperature. Under the corresponding critical strain, above 1050°C with a strain rate of 0.01–5 s−1 and 850–1050°C with the lower strain rate of 0.01 s−1, DRX can occur in the UHSS, and the dislocations of formed austenite grains increase significantly with increasing the strain.(2)
A DRX model is developed and the calculated activation energy is 504264 J·mol−1, Zener–Hollomon parameter equation is Z=ε˙exp504264/RT, and thermal processing equation is ε˙=0.6089σp6.9798exp−504264/RT.(3)
The critical strain of DRX detected by the P-J method isεc/εp=0.631, which indicates that DRX of the tested UHSS is relatively easy to occur by hot rolling process. The linear relationship of εp, εc, and ln Z is as follows: εp = 0.45ln Z−0.889 and εc = 0.028ln Z−0.567.



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