# Hot Deformation Characteristics and 3-D Processing Map of a High-Titanium Nb-Micro-alloyed Steel

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}. Using a sinh type constitutive equation, the apparent activation energy of the examined steel was 373.16 kJ/mol and the stress exponent was 6.059. The relations between Zener–Hollomon parameters versus peak stress (strain) or steady-state stress (strain) were successfully established via the Avrami equation. The dynamic recrystallization kinetics model of the examined steel was constructed and the validity was confirmed based on the experimental results. The 3-D atomic distribution maps illustrated that strain can significantly affect the values of power dissipation efficiency and the area of instability domains. The 3-D processing maps based on a dynamic material model at the strains of 0.2, 0.4, 0.6 and 0.8 were established. Based on traditional and 3-D processing maps and microstructural evaluation, the optimum parameter of for a high-titanium Nb-micro-alloyed steel was determined to be 1000–1050 °C/0.1–1 s

^{−1}.

## 1. Introduction

## 2. Examined Steel and Procedures

^{−1}) up to a true strain of 0.8. The specimens were then water quenched immediately after compression to preserve the deformed microstructure. The true stress-strain curve was obtained by transforming the load-stroke data during hot compression [25].

## 3. Results and Discussion

#### 3.1. True Stress–True Strain Curves

^{−1}and the deformation temperature is higher than 950 °C (Figure 1b), the flow stress decreases after reaching a peak stress value and then stays at a constant stress value, which indicates that the phenomenon of dynamic recrystallization (DRX) occurs. This is because the softening effect reduces the dislocation density, which leads to the decrease of flow stress. When the deformation temperature is less than 950 °C (Figure 1c), the flow stress keeps rising and then stabilizes with the increase of strain, which means that the phenomenon of dynamic recovery (DRV) occurs. It shows that the work hardening of the examined steel has played a dominant role in the hot deformation process. In short, the flow stress of materials in the process of hot deformation is affected by various factors.

#### 3.2. Constitutive Analysis

_{def}is the hot deformation activation energy (KJ/mol), σ is the strain rate (s

^{−1}), T is the absolute temperature (K), R is the universal gas constant, and finally A

_{1}, A

_{2}, A, α, β, n and n′ are the material constants.

_{p}and $\mathrm{ln}\dot{\epsilon}$ vs. σ

_{p}, respectively. As shown in Figure 3a,b, the average slopes of these curves are 8.219 and 0.0728 for n′ and β, respectively. Therefore, the value of α = β/n′ is determined as 0.0089.

_{p})] vs. $\mathrm{ln}\dot{\epsilon}$atisfies the linear relationship, as shown in Figure 3c. This illustrates that the stress index is independent of temperature and the average value of n is 6.059. The plot of ln[sinh(ασ

_{p})] vs. 1/T (as shown in Figure 4) also shows a linear relationship, and the average slope b is determined to be 7407.25. According to the intercept of fitting line in Figure 5, the value of A is 1.618 × 10

^{14}, then the hyperbolic sine constitutive model of the examined steel at a true strain of 0.8 can be expressed as follows:

_{def}= Rnb = 373.16 KJ/mol, which is consistent with similar results reported in the literature [26]. The value of Q

_{def}and the stress index n of the examined steel are higher than Ti–Nb steels tested with low titanium and low niobium content [27,28]. The values around 290 and 305 KJ/mol seem to be reasonable for activation energies for hot deformation in the case of Ti IF and Ti Nb IF steels [29]. The addition of micro-alloying elements Nb and Ti it is known to delaying recovery and preventing static recrystallization to commence, leading to a strain accumulation that can be caused or by fine particle precipitation in austenite.

#### 3.3. Characterization of DRX Behavior

^{−1}are given in Figure 6. It can be seen from the curve that as the stress increases, the strain hardening rate gradually decreases until the stress reaches the peak value, at which time the strain hardening rate drops to zero. According to Jonas et al. [30], strain hardening rate increases again as the stress decreasing, and when it reaches zero again, the stress reaches the steady-state stress (σ

_{s}).

^{n}

_{1}and Z = A″ε

^{n}

_{2}, the relations between the Z parameter and σ(ε) can be obtained. According to the above equation, the plots of lnσ

_{p}, lnε

_{p}, lnσ

_{s}and lnε

_{s}vs. lnZ are shown in Figure 7. Therefore, the relationships between peak strain or stress and steady-state strain or stress with the Z parameter are described as follows:

_{3}are the material constants. The maximum softening rate strain, ε

^{∗}and the strain required to achieve steady-state stress, ε

_{s}, are important parameters to characterize the volume fraction of DRX in hot deformation. According to some studies, it is proven that Equation (2) can be transformed as follows [32]:

_{p})/(ε

_{s}+ ε

_{p})) is almost linear at different deformation temperatures. The slope and intercept of the fitted linear equation (Figure 8) correspond to the values of the material coefficients k and n

_{3}, that is, they are 1.4847 and 3.4931, respectively. Therefore, the Avrami equation for dynamic recrystallization of examined steel is expressed as follows:

_{3}value. This is because the n

_{3}value depends on the nucleation mechanism of recrystallization and type of nucleation [33,34]. Most of the nucleation occurs in the early stage of recrystallization, and the process is easy to occur near the grain boundary, forming a so-called necklace structure after a short time [32]. In this process, high strain rate and low deformation temperature will significantly increase the starting point of DRX, that is, the critical strain value. The dynamic model of this experiment can predict the volume fraction of DRX of a high-titanium Nb-micro-alloyed steel very well.

#### 3.4. Processing Maps

#### 3.4.1. The Principles of Processing Maps

_{max}(m = 1) of the ideal linear condition, and is defined as follows [36]:

#### 3.4.2. 3-D Distribution Maps of the Power Dissipation Efficiency and Instability Parameter under Different Conditions

^{−1}, and the value of instability parameter is −3.65.

^{−1}and 1000–1100 °C. This phenomenon also validates the results of the latter observation of microstructures. The 3-D distribution map (Figure 11b) of instability parameter under strains of 0.2, 0.4, 0.6 and 0.8 was analyzed. The red area displays “instability” while the blue area mean “stability”. On the whole, as the strain increases, the area of the instability domains decreases rapidly and then increases, which is consistent with the trend of the 3-D power dissipation map. When the strain is at 0.6, the area of the instability domains is the smallest, and the instability domains are mainly located at 900–1100 °C/1–10 s

^{−1}. Comparing strain of 0.4 with strain of 0.2, it was found that the unsafe domains disappeared in the range of low temperature and strain rate. In addition, it is always safe in the region of moderate deformation temperature and strain rate under all strains.

#### 3.4.3. Processing Maps Analysis

^{−1}. Therefore, processing maps can be effectively used to evaluate the optimum processing parameters of materials [37]. However, it is necessary to discuss the relationship between the processing maps and the microstructural evolution, and it can well verify the accuracy of the prediction of the processing maps.

#### 3.4.4. Microstructural Observations

^{−1}.

^{−1}and 1050 °C/10 s

^{−1}were analyzed (Figure 15), in which a high density of dislocations was observed with a high magnification. When the deformation temperature decreases and strain rate increases, dislocations continue to occur through the source of dislocations and move to the grain boundary by sliding and climbing, which leads to the increase of dislocation density and the formation of a dislocation wall. The dislocation density near the grain boundary is higher, and the dislocation pile-up group is more obvious at high strain rates, as shown in Figure 15. This is because the dislocation pile-up near grain boundaries at high strain rates does not have enough time to be eliminated by the dynamic recovery and recrystallization. Combining Figure 11a and Figure 15, it is found that the values of power dissipation efficiency of the material are inversely related to the dislocation density. For example, the dislocation density is higher at 1050 °C/10 s

^{−1}, but the corresponding power dissipation efficiency is only 7.2%. When the strain rate drops to 0.1 s

^{−1}, the values of power dissipation efficiency at this time rises to 30.5%. Meanwhile, it also explains that the 3-D processing map can guide the evolution process of the microstructure.

## 4. Conclusions

- (1)
- Both the peak stress and flow stress increased with decreasing deformation temperature and increasing strain rate. The peak stress of a high-titanium Nb-micro-alloyed steel varied from the highest value of 219.7 MPa at 900 °C with a strain rate of 10 s
^{−1}to the lowest value of 45.4 MPa at 1100 °C with a strain rate of 0.005 s^{−1}. - (2)
- Increasing the titanium and niobium content of micro-alloyed steel can increase the activation energy of hot deformation, which may hinder the occurrence of dynamic recrystallization. For high-titanium Nb-micro-alloyed steel, the constitutive equation was determined as$$Z=\dot{\epsilon}\mathrm{exp}(373.16/RT)=1.618\times {10}^{14}{[\mathrm{sinh}(0.0089{\sigma}_{p})]}^{6.059}$$
- (3)
- The relations between the Zener–Hollomon parameters versus peak stress (strain) or steady-state stress (strain) were established via the Avrami equation. The DRX kinetics model of the examined steel was obtained as $X=1-\mathrm{exp}[-3.4931(2(\epsilon -{\epsilon}_{p})/{({\epsilon}_{s}+{\epsilon}_{p})}^{1.4847}]$. The high strain rate and low deformation temperature can significantly increase the starting point of DRX, that is, the critical strain value. A high agreement was recognizable and the kinetics model was suitable to predict the DRX process of the examined steel.
- (4)
- The power dissipation efficiency and instability maps based on the dynamic material model at the strains of 0.2, 0.4, 0.6 and 0.8 were established. The value of power dissipation efficiency and the area of instability domains vary with the increase of strain. The high η-value domain appears at 1000–1050 °C/0.1–1 s
^{−1}, and the instability domains occurred mainly in the high strain rate region (1–10 s^{−1}) and low deformation temperature and strain rate region (900–950 °C/0.005–0.1 s^{−1}). Based on the traditional and 3-D processing maps and microstructural evaluation, the optimum parameter of for a high-titanium Nb-micro-alloyed steel was at 1000–1050 °C/0.1–1 s^{−1}, and a dynamic recrystallisation structure with fine and homogeneous grain size can be obtained.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Medina, S.F.; Hernández, C.A. General expression of the Zener-Hollomon parameter as a function of the chemical composition of low alloy and micro-alloyed steels. Acta Mater.
**1996**, 44, 137–148. [Google Scholar] [CrossRef] - Mirzadeh, H.; Najafizadeh, A.; Moazeny, M. Flow curve analysis of 17-4. Metall. Mater. Trans. A
**2009**, 40, 2950–2958. [Google Scholar] [CrossRef] - Mirzadeh, H.; Cabrera, J.M.; Prado, J.M. Hot deformation behavior of a medium carbon micro-alloyed steel. Mater. Sci. Eng. A
**2011**, 528, 3876–3882. [Google Scholar] [CrossRef] - Wray, P.J. Effect of composition and initial grain size on the dynamic recrystallization of austenite in plain carbon steels. Metall. Mater. Trans. A
**1984**, 15, 2009–2019. [Google Scholar] [CrossRef] - Mirzadeh, H. Quantification of the strengthening effect of reinforcements during hot deformation of aluminum-based composites. Mater. Des.
**2015**, 65, 80–92. [Google Scholar] [CrossRef] - Mirzadeh, H. Constitutive modeling and prediction of hot deformation flow stress under dynamic recrystallization conditions. Mech. Mater.
**2015**, 85, 66–79. [Google Scholar] [CrossRef] - Mirzadeh, H. Constitutive analysis of Mg–Al–Zn magnesium alloys during hot deformation. Mech. Mater.
**2014**, 77, 80–85. [Google Scholar] [CrossRef] - Raj, R. Development of a processing map for use in warm-forming and hot-forming processes. Metall. Trans. A
**1981**, 12, 1089–1097. [Google Scholar] [CrossRef] - Gegel, H.L.; Prasad, Y.V.R.K.; Doraivelu, S.M. Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242. Metall. Trans. A
**1984**, 15, 1883–1892. [Google Scholar] - Babu, K.A.; Mandal, S.; Kumar, A. Characterization of hot deformation behavior of alloy 617 through kinetic analysis, dynamic material modeling and microstructural studies. Mater. Sci. Eng. A
**2016**, 664, 177–187. [Google Scholar] [CrossRef] - Wen, D.X.; Lin, Y.C.; Li, H.B. Hot deformation behavior and processing map of a typical Ni-based superalloy. Mater. Sci. Eng. A
**2014**, 591, 183–192. [Google Scholar] [CrossRef] - Momeni, A.; Dehghani, K. Characterization of hot deformation behavior of 410 martensitic stainless steel using constitutive equations and processing maps. Mater. Sci. Eng. A
**2010**, 527, 5467–5473. [Google Scholar] [CrossRef] - Bobbili, R.; Madhu, V. An investigation into hot deformation characteristics and processing maps of high-strength armor steel. J. Mater. Eng. Perform.
**2015**, 24, 4728–4735. [Google Scholar] [CrossRef] - Yang, Z.; Zhang, F.; Zheng, C. Study on hot deformation behaviour and processing maps of low carbon bainitic steel. Mater. Des.
**2015**, 66, 258–266. [Google Scholar] [CrossRef] - Petr, O.; Petr, K.; Rostislav, K.; Pavol, B. Extension of experimentally assembled processing maps of 10CrMo9-10 steel via a predicted dataset and the influence on overall informative possibilities. Metals
**2019**, 9, 1218. [Google Scholar] - Prasad, Y.V.R.K.; Seshacharyulu, T. Processing maps for hot working of titanium alloys. Mater. Sci. Eng. A
**1998**, 243, 82–88. [Google Scholar] [CrossRef] - Fan, J.K.; Kou, H.C.; Lai, M.J. Characterization of hot deformation behavior of a new near beta titanium alloy: Ti-7333. Mater. Des.
**2013**, 49, 945–952. [Google Scholar] [CrossRef] - Saxena, K.K.; Sonkar, S.; Pancholi, V. Hot deformation behavior of Zr-2.5Nb alloy: A comparative study using different materials models. J. Alloy. Compd.
**2016**, 662, 94–101. [Google Scholar] [CrossRef] - Rao, K.P.; Prasad, Y.V.R.K.; Suresh, K. Materials modeling and simulation of isothermal forging of rolled AZ31B magnesium alloy: Anisotropy of flow. Mater. Des.
**2011**, 32, 2545–2553. [Google Scholar] [CrossRef] - Prasad, Y.V.R.K.; Rao, K.P. Effect of homogenization on the hot deformation behavior of cast AZ31 magnesium alloy. Mater. Des.
**2009**, 30, 3723–3730. [Google Scholar] [CrossRef] - Gao, Y.; Xuan, Y.; Ly, X.; Yang, S. Hot deformation behaviors of the Mg-3Sn-2Al-1Zn alloy: Investigation on its constitutive equation, processing map, and microstructure. Materials
**2020**, 13, 312. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gao, Y.; Xuan, Y.; Lia, C.; Yang, S. Characterization of hot deformation behavior and processing maps of Mg-3Sn-2Al-1Zn-5Li magnesium alloy. Metals
**2019**, 9, 1262. [Google Scholar] [CrossRef] [Green Version] - Samal, S.; Rahul, M.R.; Kottada, R.S. Hot deformation behaviour and processing map of Co-Cu-Fe-Ni-Ti eutectic high entropy alloy. Mater. Sci. Eng. A
**2016**, 664, 227–235. [Google Scholar] [CrossRef] - Rajput, S.K.; Chaudhari, G.P.; Nath, S.K. Physical simulation of hot deformation of low-carbon Ti-Nb micro-alloyed steel and microstructural studies. J. Mater. Eng. Perform.
**2014**, 23, 2930–2942. [Google Scholar] [CrossRef] - Samantaray, D.; Mandal, S.; Bhaduri, A.K. A critical comparison of various data processing methods in simple uni-axial compression testing. Mater. Des.
**2011**, 32, 2797–2802. [Google Scholar] [CrossRef] - Bao, S.; Zhao, G.; Yu, C. Recrystallization behavior of a Nb-micro-alloyed steel during hot compression. Appl. Math. Model.
**2011**, 35, 3268–3275. [Google Scholar] [CrossRef] - Fernández, A.I.; Uranga, P.; López, B. Dynamic recrystallization behavior covering a wide austenite grain size range in Nb and Nb–Ti micro-alloyed steels. Mater. Sci. Eng. A
**2003**, 361, 367–376. [Google Scholar] [CrossRef] - Li, M.Q.; Zhen, L.Y.; Si, J.H.; Xiang, Y.Q.; Di, W. Effect of niobium and titanium on dynamic recrystallization behavior of low carbon steels. J. Iron Steel Res. Int.
**2008**, 15, 31–36. [Google Scholar] - Lino, R.; Guadanini, L.G.L.; Silva, L.B.; Neto, J.G.C.; Barbosa, R. Effect of Nb and Ti addition on activation energy for austenite hot deformation. J. Mater. Res. Technol.
**2019**, 8, 180–188. [Google Scholar] [CrossRef] - Jonas, J.J.; Quelennec, X.; Jiang, L. The Avrami kinetics of dynamic recrystallization. Acta Mater.
**2009**, 57, 2748–2756. [Google Scholar] [CrossRef] - Cho, S.H.; Yoo, Y.C. Hot rolling simulations of austenitic stainless steel. J. Mater. Sci.
**2001**, 36, 4267–4272. [Google Scholar] [CrossRef] - Momeni, A.; Arabi, H.; Rezaei, A. Hot deformation behavior of austenite in HSLA-100 micro-alloyed steel. Mater. Sci. Eng. A
**2011**, 528, 2158–2163. [Google Scholar] [CrossRef] - Dieter, G.E.; Kuhn, H.A.; Semiatin, S.L. Handbook of Work Ability and Process Design; ASM: Materials Park, OH, USA, 2003; pp. 35–44. [Google Scholar]
- Humphreys, F.J.; Hatherly, M. Recrystallization and Related Annealing Phenomena, 2nd ed.; Anthony Rollett: Pergamon, The Netherlands, 2004; pp. 232–239. [Google Scholar]
- Momeni, A.; Dehghani, K. Hot working behavior of 2205 austenite-ferrite duplex stainless steel characterized by constitutive equations and processing maps. Mater. Sci. Eng. A
**2011**, 528, 1448–1454. [Google Scholar] [CrossRef] - Murty, N.; Raoa, N.; Kashyap, B.P. On the hot working characteristics of 2014 Al-20 vol % Al
_{2}O_{3}metal matrix composite. J. Mater. Process. Technol.**2005**, 166, 279–285. [Google Scholar] [CrossRef] - Rajput, S.K.; Chaudhari, G.P.; Nath, S.K. Characterization of hot deformation behavior of a low carbon steel using processing maps, constitutive equations and Zener-Hollomon parameter. J. Mater. Process. Technol.
**2016**, 237, 113–125. [Google Scholar] [CrossRef]

**Figure 1.**Flow curves of the examined steel at different temperatures and strain rates of (

**a**) 0.005 s

^{−1}, (

**b**) 0.1 s

^{−1}, (

**c**) 1 s

^{−1}and (

**d**) 10 s

^{−1}.

**Figure 2.**Relation between peak flow stress with (

**a**) ln (strain rate) and (

**b**) deformation temperatures.

**Figure 3.**Relations between (

**a**) ln(strain rate) and lnσ

_{p}, (

**b**) ln(strain rate) and σ

_{p}, and (

**c**) ln(strain rate) and ln[sinh(ασ

_{p})] at different temperatures.

**Figure 7.**Relations between (

**a**) peak stress and Z, (

**b**) steady-state stress and Z, (

**c**) peak strain and Z and (

**d**) steady-state strain and Z.

**Figure 10.**Three-D atomic distribution maps of value of (

**a**) power dissipation efficiency and (

**b**) instability parameter under different conditions.

**Figure 11.**Three-D distribution maps of (

**a**) power dissipation efficiency and (

**b**) instability parameter under different conditions.

**Figure 12.**Processing maps of a high-titanium Nb-micro-alloyed steel obtained by superposition of the PDM and the instability map under true strains: (

**a**) 0.6 and (

**b**) 0.8.

**Figure 13.**LM micrographs of the examined steel under deformation conditions of (

**a**) 1000 °C and 0.005 s

^{−1}and (

**b**) 1050 °C and 10 s

^{−1}.

**Figure 14.**LM micrographs of the examined steel after hot deformation under different conditions: (

**a**) 950 °C and 0.005 s

^{−1}, (

**b**) 950 °C and 10 s

^{−1}, (

**c**) 1050 °C and 0.1 s

^{−1}and (

**d**) 1000 °C and 0.1 s

^{−1}.

**Figure 15.**The TEM micrographs of Nb–Ti micro-alloyed steel at different conditions: (

**a**) 1050 °C and 0.1 s

^{−1}and (

**b**) 1050 °C and 10 s

^{−1}.

Elements | C | Mn | Ti | Nb | Si | N | S | Al | Cr | Fe |
---|---|---|---|---|---|---|---|---|---|---|

Composition | 0.093 | 1.54 | 0.104 | 0.078 | 0.3 | 0.0051 | 0.0056 | 0.013 | 0.43 | Bal. |

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**MDPI and ACS Style**

Qian, P.; Tang, Z.; Wang, L.; Siyasiya, C.W.
Hot Deformation Characteristics and 3-D Processing Map of a High-Titanium Nb-Micro-alloyed Steel. *Materials* **2020**, *13*, 1501.
https://doi.org/10.3390/ma13071501

**AMA Style**

Qian P, Tang Z, Wang L, Siyasiya CW.
Hot Deformation Characteristics and 3-D Processing Map of a High-Titanium Nb-Micro-alloyed Steel. *Materials*. 2020; 13(7):1501.
https://doi.org/10.3390/ma13071501

**Chicago/Turabian Style**

Qian, Pingping, Zhenghua Tang, Li Wang, and Charles W. Siyasiya.
2020. "Hot Deformation Characteristics and 3-D Processing Map of a High-Titanium Nb-Micro-alloyed Steel" *Materials* 13, no. 7: 1501.
https://doi.org/10.3390/ma13071501