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Characterization of hot deformation behavior of a new microalloyed C–Mn–Al high-strength steel
Materials Science & Engineering A 564 (2013) 140–146
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Characterization of hot deformation behavior of a new microalloyed C–Mn–Al high-strength steel Hai-lian Wei a, Guo-quan Liu a,b,n, Xiang Xiao a, Hai-tao Zhao a, Hang Ding a, Ren-mu Kang a,c a
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China c Sichuan Chuanwei Co. Ltd., Chengdu 610100, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 October 2012 Received in revised form 25 November 2012 Accepted 26 November 2012 Available online 1 December 2012
The compressive deformation behaviors of a new 0.23C–1.50Mn–1.79Al (wt%) based microalloyed high-strength steel were investigated at the temperatures from 900 1C to 1100 1C and strain rates from 0.01 s 1 to 30 s 1 on a Gleeble-1500 thermo-simulation machine. The flow stress constitutive equation of hot deformation for this steel was developed with the activation energy Q being about 310 kJ/mol. Activation energy analysis showed that high Al addition in this steel seemed not to affect the activation energy much. A regression expression proposed by Medina and Hernandez [24] to predict the Q value of microalloyed steels was found to have a relative error 2.58% for this steel. The dynamic recrystallization (DRX) analysis showed that the DRX behavior of the experimental steel was evidently affected by both the deformation temperature and the strain rate. The dependence of steady-state grain size, the peak strain and the peak stress on Zener–Hollomon parameter of this steel was plotted and found that the values of Zener–Hollomon exponents of this steel was in reasonable agreement with microalloyed steels without high Al addition. & 2012 Elsevier B.V. All rights reserved.
Keywords: C–Mn–Al microalloyed steel Hot deformation Constitutive analysis Dynamic recrystallization (DRX)
1. Introduction In order to save energy as well as to protect environment, there is an urgent need to develop high strength steels with good toughness, including TRIP steels. Conventional TRIP steels were developed based on the C–Mn–Si alloy system. Nowadays, C–Mn– Al–Si or C–Mn–Al based TRIP steels which reduce or remove the harmful effects of Si on galvanizability with good mechanical properties and better galvanizability have attracted more and more attention [1–10]. The characteristics of microstructural development, mechanical behavior of TRIP steels with Al addition and the effect of Al addition on them have been extensively investigated [1,7–10]. However, there is very little detailed literature concerning the hot deformation behavior of TRIP steels with high Al addition ( 41.5 wt% Al). So this work is focused on the hot deformation behavior of a new low carbon microalloyed C–Mn–Al based steel and investigates the effects of deformation temperature and strain rate on the hot deformation characteristics of this steel by hot compression tests. The constitutive equations describing the dependence of the flow stress on the strain, strain rate and temperature are
n Corresponding author at: School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China. E-mail address: [email protected] (G.-q. Liu).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.099
developed. The dynamic recrystallization (DRX) behavior of this steel is also investigated with both the microstructure observation and the flow stress analysis.
2. Experimental material and procedures The chemical composition of the material used in this investigation is given in Table 1. The experimental steel was melted and casted into an ingot of 50 kg in vacuum induction furnace, then hot forged and rolled to 20 mm thick plate. The plate was heated at 1000 1C for 2 h followed by air-cooling in order to refine the grains and homogenize the microstructure. Cylindrical specimens of 8 mm in diameter and 15 mm in length were machined from the plate. The compression tests were carried out on a Gleeble-1500 thermo-mechanical simulator in the temperature range from 900 1C to 1100 1C at an interval of 50 1C and at constant true strain rates of 0.01, 0.1, 1, 10 and 30 s 1, respectively. This wide range of conditions provided a good description of the hot flow behaviors of steels. Prior to the compression, specimens were heated in vacuum at the rate of 10 K s 1 to 1150 1C for 5 min and then cooled to the deformation temperature with the cooling rate of 6.7 K s 1. All specimens were kept at the test temperature for 30 s before compression in order to homogenize the temperature. Specimens were deformed to a strain of 1.0, and then they were water quenched immediately to
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Table 1 Chemical composition of the experimental steel (wt%). C
Si
Al
Mn
Cr
Mo
B
Ni
Nb
Ti
S
P
N
0.23
o0.10
1.79
1.50
1.0
0.25
0.006
1.0
0.06
0.025
0.0024
0.0084
0.0019
hardening and the dynamic softening [11,12]. At the beginning of deformation, the work hardening exceeds the dynamic softening due to the rapid multiplication of dislocations, leading to an increase of flow stress. As the strain increases, dynamic softening mechanisms such as dynamic recovery and dynamic recrystallization begin to work, which can offset or partially offset the effect of work hardening. If the rate of dynamic softening is higher than the rate of work hardening, the flow stress decreases gradually. And when a new balance between softening and hardening is obtained, the steady state will reach. From Fig. 1, one can also see that the flow stress of the experimental steel increases with the decrease of temperature and the increase of strain rate. This is because low strain rates and high temperatures can provide longer time for energy accumulation and enable higher mobilities for nucleation and growth of dynamically recrystallized grains and dislocation annihilation, so the flow stress is reduced [13]. The variation of flow stress with deformation temperatures and strain rates can be seen more clearly in Fig. 2, where the flow stress at a true strain of 0.7 is plotted as a function of the deformation temperature and the logarithm of the strain rate, respectively. 3.2. Constitutive analysis In order to further investigate the hot deformation behaviors of the experimental steel, it is necessary to study the constitutive characteristics. The effects of the temperature and strain rate on the deformation behaviors can be represented by Zener– Hollomon parameter, Z, in an exponent-type equation (Eq. (1)). The power law description of stress (Eq. (2)) is preferred for relatively low stresses when as o0.8, while the exponential law (Eq. (3)) is suitable for high stresses when as 41.2, and the hyperbolic sine law (Eq. (4)) can be used for a wide range of stresses and gives better approximations between Z parameter and flow stress [14–16]. Q ð1Þ Z ¼ e_ exp RT Fig. 1. Flow curves obtained at different deformation conditions: (a) 1000 1C; and (b) 0.01 s 1.
room temperature in order to remain the hot deformation microstructure. The deformed specimens were sectioned through the longitudinal axis, then polished and chemically etched with a saturated aqueous picric acid solution to reveal the microstructure.
e_ ¼ A1 sn1 exp
Q RT
e_ ¼ A2 expðbsÞexp
Q RT
e_ ¼ A½sin hðasÞn exp 3. Results and discussion 3.1. True stress and true strain Fig. 1 shows the stress–strain curves of the steel deformed at different temperatures and strain rates. From the experimental results, it can be found that the steel exhibits a typical DRX behavior under higher temperatures (higher than 1000 1C) and lower strain rates (lower than 1 s 1), the stress rising to a peak followed by softening toward a steady state region. As well know, the hot deformation process is a competing process of the work
ð2Þ
Q RT
ð3Þ ð4Þ
In Eq. (4), e_ is the strain rate (s 1), R is the universal gas constant (8.3145 J mol 1 K 1), T is the absolute temperature (K), Q is the activation energy of hot deformation (J mol 1), A, a and n are the material constants, s is the flow stress (MPa). Characteristic stresses such as peak stress, steady state stress, or stress corresponding to a specific strain can be used to establish these equations [17–19]. Since the steady state stress may not be precisely attained or there may be some softening due to morphological evolution [20], in addition, the peak stress is more important for industrial processes [21], so in this paper peak stress was chosen to calculate Q value.
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Fig. 2. Relationship between flow stress at a true strain of 0.7 and (a) the deformation temperature; (b) the logarithm of the strain rate.
The value of a can be calculated from a ¼ b/n1, with the value of n1 and b in Eq. (2) and Eq. (3) obtained from the slope of the lines ln e_ ln s and ln e_ s plots, respectively [22,23]. Fig. 3 shows both the experimental data and regression results of ln e_ sp (Fig. 3(a)) and ln e_ ln sp (Fig. 3(b)) plots, and a mean value of n1 and b at different temperatures can be computed as 6.85206 and 0.068543, respectively, so a ¼0.01. Taking natural logarithms on both sides of Eq. (4), Eq. (5) can be obtained. Q 1 @ðlne_ Þ ¼ n@ lnsinhðasÞ @ ð5Þ R T For constant T, Eq. (5) can be rewritten into Eq. (6). 1 @ ln½sinhðasÞ ¼ n @ lne_
ð6Þ
In accordance with the relationship curves of ln[sinh(asp)] and ln e_ (Fig. 4a), the average value of n can be estimated to be 5.2035. According to Eq. (5), Eq. (7) can be obtained. Q ¼ Rn
@ ln½sinhðasÞ @ 1=T
ð7Þ
In accordance with the relationship curves of ln[sinh(asp)] and 1/T (Fig. 4b), the average value of the slopes is 7155.554. So the value of Q can be obtained as 309.583 kJ/mol using Eq. (7). Then A
Fig. 3. Relationships between strain rates and peak stresses: (a) ln e_ and sp; (b) ln e_ and ln sp.
can be easily obtained as 8.1264 1010. Finally, substituting the values of n, A and Q into Eq. (1) and Eq. (4), the peak stress constitutive equation of hot deformation for the experimental steel can be expressed as Eq. (8). Z ¼ e_ exp 309583=RT ¼ 8:1264 1010 ðsinh 0:01sp Þ5:2035 ð8Þ Q is an important material parameter serving as an indicator of deformation difficulty in hot deformation. There are some regression expressions corresponding to chemical composition to predict the Q value. One of the expressions to calculate the Q value of microalloyed steels was proposed by Medina and Hernandez [24], Q J=mol ¼ 2670002535:52ðC%Þ þ1010ðMn%Þ þ33620:76ðSi%Þ þ35651:28ðMo%Þ þ93680:52ðTi%Þ0:5919 þ 31673:46ðV%Þ þ70729:85ðNb%Þ0:5649
ð9Þ
where (%) depicts the total content of the given elements in the studied steel. Table 2 lists both the experimental activation energy Qexp and calculated activation energy Qcal by Eq. (9) of some microalloyed steels [15,24,25] and the experimental activation energy Qexp of some stainless steels [26–30], the a value in Eq. (4) is also listed in Table 2.
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Table 2 The a value and activation energy of some microalloyed steels and stainless steels obtained by compression or torsion testing.
a (M Pa 1)
Qexp (kJ/mol)
Qcal (kJ/mol)
DQ Q exp
0.2–50 s 1 0.2–50 s 1 0.2–50 s 1 0.001–0.5 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.01–30 s 1
0.012 0.012 0.012 0.0091 0.011875 0.011875 0.011875 0.011875 0.011875 0.01
312 325 326 320 285.2 294 296.5 287.8 294.5 310
284 297 297 305 285.3 293.8 296.7 287.8 294.5 302
8.97 8.62 8.89 4.69 0.035 0.068 0.068 0 0 2.58
0.0001–10 s 1 0.001–1 s 1 0.01–10 s 1 0.001–1 s 1 0.001–1 s 1
0.0105 0.012 0.00579 0.007 0.011
460 479 518 460 448
Materials
Test
Deforming condition
C–Mn–Ti C–Mn–Nb–Ti C–Mn–Nb–Ti–B C–Mn–V C–Mn–0.021Ti C–Mn–0.055Ti C–Mn–0.075Ti C–Mn–0.041Nb C–Mn–0.093Nb C–Mn–Nb–Ti–Al
Compression Compression Compression Compression Torsion Torsion Torsion Torsion Torsion Compression
800–1200 1C, 800–1200 1C, 800–1200 1C, 850–1100 1C, 900–1100 1C, 900–1100 1C, 900–1100 1C, 850–1100 1C, 850–1100 1C, 900–1100 1C,
PH stainless steel 2205 duplex stainless steel 316LN stainless steel PH stainless steel 410 martensitic stainless steel
Compression Compression Compression Compression Compression
900–1150 1C, 950–1200 1C, 900–1200 1C, 900–1100 1C, 900–1150 1C,
ð%Þ
Ref [25] [25] [25] [15] [24] [24] [24] [24] [24] This study [26] [27] [28] [29] [30]
The stress multiplier a is an adjustable constant which brings as into the correct range that gives linear and parallel lines in ln e_ vs. ln[sinh(as)]plots. It is found that the a values of microalloyed steels (including the experimental steel) listed in Table 2 are close to 0.012 M Pa 1, and the a values of stainless steels are in a wider range around 0.011 M Pa 1 (from 0.00579 to 0.012) in Table 2, which is in reasonable agreement with McQueen et al. [31] who indicated that the value of a had generally been 0.014 M Pa 1 for the HSLA steels and 0.012 M Pa 1 for stainless steels. The Q value of the experimental steel is close to that of austenite self-diffusion and equals well with Q values both in the creep and hot-working ranges [32–34], and it is also in reasonable agreement with that of microalloyed steels in the literature listed in Table 2. It seems that the high Al content in the experimental steel does not affect the activation energy much. On the other hand, the activation energy of stainless steels is much higher than that of microalloyed steels as seen in Table 2, which is due to the high solute content of Cr, Mo and Ni additions in stainless steels. At the same time, the calculated Qcal of the microalloyed steels is often lower than the measured value of Qexp as shown in Table 2. This is probably because some chemical elements such as Cr, Ni, B, Cu and Al in these steels were not considered in the Medina’s expression, which leads to the deviation between Qexp and Qcal. However, the relative error of all the calculated Q value in Table 2 is less than 10% (for the experimental steel, the relative error is 2.58%). It suggests that Eq. (9) can be applied to obtain a first approximation of Q values of microalloyed steels, if no better equation available.
3.3. DRX analysis Microstructures of the experimental steel deformed at different conditions to a strain of 1.0 are shown in Figs. 5 and 6. It can be seen from Fig. 5 that at the temperature of 900 1C and strain rate of 10 s 1, we can see that the original grains were elongated along the deformation direction. As the temperature increased to 950 1C, the original grains were elongated along the deformation direction, moreover, there are a few new fine grains were nucleated at the serrated part of initial grain boundaries, demonstrating occurrence of DRX. As the temperature increased to 1000 1C, more new fine DRX grains emerged at prior grain boundaries, and the necklace structure started to form, as seen in Fig. 5c. As the deformation temperature further increased to 1050 1C, the volume fraction of the recrystallized grains increased
Fig. 4. Relationship between (a) ln[sinh(asp)] and ln e_ ; (b) ln[sinh(asp)] and 1/T.
dramatically, and the majority of the original grains were replaced by new fine DRX grains. From Fig. 6, it can be seen that at the temperature of 1000 1C and strain rate of 30 s 1, the original grains were elongated along the deformation direction, a few new DRX grains were nucleated at the serrated part of initial grain boundaries, demonstrating occurrence of the DRX. As the strain rate decreased to 1 s 1, more
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H.l. Wei et al. / Materials Science & Engineering A 564 (2013) 140–146
Fig. 5. Optical deformed microstructures at a strain of 1.0 under different temperatures at 10 s 1: (a) 900 1C; (b) 950 1C; (c) 1000 1C and (d) 1050 1C.
Fig. 6. Optical deformed microstructures at a strain of 1.0 under different conditions: (a) 1000 1C, 30 s 1; (b) 1000 1C, 1 s 1; (c) 1000 1C, 0.1 s 1 and (d) 1100 1C, 0.01 s 1.
new fine DRX grains emerged at prior grain boundaries. As the strain rate decreased to 0.1 s 1, the volume fraction of the recrystallized grains increased dramatically, and the original grains were replaced completely by new fine DRX grains, the DRX process had been completed, as seen in Fig. 6c. Fig. 6d shows the microstructure of the specimen deformed at 1100 1C and 0.01 s 1. It can be seen that as the deformation temperature
increased to 1100 1C and the strain rate decreased to 0.01 s 1, the DRX grains coarsened obviously. From the analysis above, it is known that the DRX is dependent sensitively on the deformation temperature and strain rate in the experimental steel. Both effects of deformation temperature and strain rate on the DRX process can be summed up in Z parameter. Decreasing of Z value, that is increasing deformation temperature
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145
Fig. 7. Relationship between Ds and Z.
and/or decreasing strain rate, leads to more adequate proceeding of DRX. The previous researchers concluded that the steady state grain size is independent on the initial grain size and remains almost unchanged at strains over the onset of steady state flow [35,36]. In this research, the steady state grain size was measured under various deformation conditions and found that it decreased with the increase in strain rate and the decrease in temperature. To model the dependence of the steady state grain size on temperature and strain rate, the following relationship is used. Ds ¼ BZ k
ð10Þ
Fig. 7 and Eq. (11) show the relationship between the steady state grain size Ds and Zener–Hollomon parameter Z of the experimental steel. lnDs ¼ 0:2005 lnZ þ 7:2644
ð11Þ
The Zener–Hollomon exponent k¼0.2005 is within the scatter of those reported in the literature: 0.13 [37], 0.167 [38], 0.193 [39] and 0.27 [40] for microalloyed steels without high Al addition. The peak strain ep is an important parameter. The critical strain ec at which dynamic recrystallization begins can be approximately determined by the peak strain ep. Therefore, peak strain can be used to estimate whether the deformed austenite will dynamically recrystallize and what percentage of the volume has recrystallized [41]. For the experimental steel, ep is also dependent on Zener– Hollomon parameter Z according to Fig. 8(a) and Eq. (12). lnep ¼ 0:0995 lnZ3:4632
ð12Þ
The Zener–Hollomon exponent 0.0995 is close to those values in the range 0.12–0.22 reported by other workers for microalloyed steels and stainless steels [25,42]. For Nb steel and 17–4 PH stainless steel, the low values of 0.09 and 0.11 have also been reported [43,44]. At the same time, the relationship between sp and Z is also plotted (Fig. 8(b)) and a relationship is obtained in Eq. (13). lnsp ¼ 0:1459 lnZ þ 0:7984
ð13Þ
The Zener–Hollomon exponent 0.1459 is also close to previous reports such as 0.147 [14] and 0.14 [45]for microalloyed steels without high Al addition. From the analysis above, it can be seen that the values of those Zener–Hollomon exponents of the steady state grain size, the peak strain and the peak stress for the experimental steel were in reasonable agreement with other microalloyed steels without
Fig. 8. Relationship between (a) ep and Z; (b) sp and Z.
high Al addition, so it is inferred that the high Al addition in microalloyed steels may not affect much the values of those Zener–Hollomon exponents.
4. Conclusions (1) The flow stress constitutive equation of the experimental steel was developed. The activation energy of hot working is about 310 kJ/mol, which is in reasonable agreement with those reported before. (2) A regression expression proposed by Medina et al. to predict the Q value of microalloyed steel was found to have a relative error 2.58% for this steel, and can be used for first approximations. (3) Microstructure examination shows that DRX behavior of this steel is dependent sensitively on the deformation temperature and strain rate, increasing deformation temperature and/ or decreasing strain rate will lead to more adequate proceeding of DRX. (4) The steady state grain size of the experimental steel increases with the increase of temperature and decrease of the strain rate in the form of ln Ds ¼ 0.2005 ln Z þ7.2644. The Zener– Hollomon exponent 0.2005 is within the scatter of those reported for microalloyed steels without high Al addition. (5) For the experimental steel, the dependence of ep and sp on Zener–Hollomon parameter Z has the form of ln ep ¼0.0995
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ln Z 3.4632 and ln sp ¼0.1459 ln Zþ0.7984. The Zener– Hollomon exponents 0.0995 and 0.1459 are in agreement with values in the range reported by other workers for microalloyed steels without high Al addition.
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Characterization of hot deformation behavior of a new microalloyed C–Mn–Al high-strength steel Hai-lian Wei a, Guo-quan Liu a,b,n, Xiang Xiao a, Hai-tao Zhao a, Hang Ding a, Ren-mu Kang a,c a
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China c Sichuan Chuanwei Co. Ltd., Chengdu 610100, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 October 2012 Received in revised form 25 November 2012 Accepted 26 November 2012 Available online 1 December 2012
The compressive deformation behaviors of a new 0.23C–1.50Mn–1.79Al (wt%) based microalloyed high-strength steel were investigated at the temperatures from 900 1C to 1100 1C and strain rates from 0.01 s 1 to 30 s 1 on a Gleeble-1500 thermo-simulation machine. The flow stress constitutive equation of hot deformation for this steel was developed with the activation energy Q being about 310 kJ/mol. Activation energy analysis showed that high Al addition in this steel seemed not to affect the activation energy much. A regression expression proposed by Medina and Hernandez [24] to predict the Q value of microalloyed steels was found to have a relative error 2.58% for this steel. The dynamic recrystallization (DRX) analysis showed that the DRX behavior of the experimental steel was evidently affected by both the deformation temperature and the strain rate. The dependence of steady-state grain size, the peak strain and the peak stress on Zener–Hollomon parameter of this steel was plotted and found that the values of Zener–Hollomon exponents of this steel was in reasonable agreement with microalloyed steels without high Al addition. & 2012 Elsevier B.V. All rights reserved.
Keywords: C–Mn–Al microalloyed steel Hot deformation Constitutive analysis Dynamic recrystallization (DRX)
1. Introduction In order to save energy as well as to protect environment, there is an urgent need to develop high strength steels with good toughness, including TRIP steels. Conventional TRIP steels were developed based on the C–Mn–Si alloy system. Nowadays, C–Mn– Al–Si or C–Mn–Al based TRIP steels which reduce or remove the harmful effects of Si on galvanizability with good mechanical properties and better galvanizability have attracted more and more attention [1–10]. The characteristics of microstructural development, mechanical behavior of TRIP steels with Al addition and the effect of Al addition on them have been extensively investigated [1,7–10]. However, there is very little detailed literature concerning the hot deformation behavior of TRIP steels with high Al addition ( 41.5 wt% Al). So this work is focused on the hot deformation behavior of a new low carbon microalloyed C–Mn–Al based steel and investigates the effects of deformation temperature and strain rate on the hot deformation characteristics of this steel by hot compression tests. The constitutive equations describing the dependence of the flow stress on the strain, strain rate and temperature are
n Corresponding author at: School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China. E-mail address: [email protected] (G.-q. Liu).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.099
developed. The dynamic recrystallization (DRX) behavior of this steel is also investigated with both the microstructure observation and the flow stress analysis.
2. Experimental material and procedures The chemical composition of the material used in this investigation is given in Table 1. The experimental steel was melted and casted into an ingot of 50 kg in vacuum induction furnace, then hot forged and rolled to 20 mm thick plate. The plate was heated at 1000 1C for 2 h followed by air-cooling in order to refine the grains and homogenize the microstructure. Cylindrical specimens of 8 mm in diameter and 15 mm in length were machined from the plate. The compression tests were carried out on a Gleeble-1500 thermo-mechanical simulator in the temperature range from 900 1C to 1100 1C at an interval of 50 1C and at constant true strain rates of 0.01, 0.1, 1, 10 and 30 s 1, respectively. This wide range of conditions provided a good description of the hot flow behaviors of steels. Prior to the compression, specimens were heated in vacuum at the rate of 10 K s 1 to 1150 1C for 5 min and then cooled to the deformation temperature with the cooling rate of 6.7 K s 1. All specimens were kept at the test temperature for 30 s before compression in order to homogenize the temperature. Specimens were deformed to a strain of 1.0, and then they were water quenched immediately to
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Table 1 Chemical composition of the experimental steel (wt%). C
Si
Al
Mn
Cr
Mo
B
Ni
Nb
Ti
S
P
N
0.23
o0.10
1.79
1.50
1.0
0.25
0.006
1.0
0.06
0.025
0.0024
0.0084
0.0019
hardening and the dynamic softening [11,12]. At the beginning of deformation, the work hardening exceeds the dynamic softening due to the rapid multiplication of dislocations, leading to an increase of flow stress. As the strain increases, dynamic softening mechanisms such as dynamic recovery and dynamic recrystallization begin to work, which can offset or partially offset the effect of work hardening. If the rate of dynamic softening is higher than the rate of work hardening, the flow stress decreases gradually. And when a new balance between softening and hardening is obtained, the steady state will reach. From Fig. 1, one can also see that the flow stress of the experimental steel increases with the decrease of temperature and the increase of strain rate. This is because low strain rates and high temperatures can provide longer time for energy accumulation and enable higher mobilities for nucleation and growth of dynamically recrystallized grains and dislocation annihilation, so the flow stress is reduced [13]. The variation of flow stress with deformation temperatures and strain rates can be seen more clearly in Fig. 2, where the flow stress at a true strain of 0.7 is plotted as a function of the deformation temperature and the logarithm of the strain rate, respectively. 3.2. Constitutive analysis In order to further investigate the hot deformation behaviors of the experimental steel, it is necessary to study the constitutive characteristics. The effects of the temperature and strain rate on the deformation behaviors can be represented by Zener– Hollomon parameter, Z, in an exponent-type equation (Eq. (1)). The power law description of stress (Eq. (2)) is preferred for relatively low stresses when as o0.8, while the exponential law (Eq. (3)) is suitable for high stresses when as 41.2, and the hyperbolic sine law (Eq. (4)) can be used for a wide range of stresses and gives better approximations between Z parameter and flow stress [14–16]. Q ð1Þ Z ¼ e_ exp RT Fig. 1. Flow curves obtained at different deformation conditions: (a) 1000 1C; and (b) 0.01 s 1.
room temperature in order to remain the hot deformation microstructure. The deformed specimens were sectioned through the longitudinal axis, then polished and chemically etched with a saturated aqueous picric acid solution to reveal the microstructure.
e_ ¼ A1 sn1 exp
Q RT
e_ ¼ A2 expðbsÞexp
Q RT
e_ ¼ A½sin hðasÞn exp 3. Results and discussion 3.1. True stress and true strain Fig. 1 shows the stress–strain curves of the steel deformed at different temperatures and strain rates. From the experimental results, it can be found that the steel exhibits a typical DRX behavior under higher temperatures (higher than 1000 1C) and lower strain rates (lower than 1 s 1), the stress rising to a peak followed by softening toward a steady state region. As well know, the hot deformation process is a competing process of the work
ð2Þ
Q RT
ð3Þ ð4Þ
In Eq. (4), e_ is the strain rate (s 1), R is the universal gas constant (8.3145 J mol 1 K 1), T is the absolute temperature (K), Q is the activation energy of hot deformation (J mol 1), A, a and n are the material constants, s is the flow stress (MPa). Characteristic stresses such as peak stress, steady state stress, or stress corresponding to a specific strain can be used to establish these equations [17–19]. Since the steady state stress may not be precisely attained or there may be some softening due to morphological evolution [20], in addition, the peak stress is more important for industrial processes [21], so in this paper peak stress was chosen to calculate Q value.
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Fig. 2. Relationship between flow stress at a true strain of 0.7 and (a) the deformation temperature; (b) the logarithm of the strain rate.
The value of a can be calculated from a ¼ b/n1, with the value of n1 and b in Eq. (2) and Eq. (3) obtained from the slope of the lines ln e_ ln s and ln e_ s plots, respectively [22,23]. Fig. 3 shows both the experimental data and regression results of ln e_ sp (Fig. 3(a)) and ln e_ ln sp (Fig. 3(b)) plots, and a mean value of n1 and b at different temperatures can be computed as 6.85206 and 0.068543, respectively, so a ¼0.01. Taking natural logarithms on both sides of Eq. (4), Eq. (5) can be obtained. Q 1 @ðlne_ Þ ¼ n@ lnsinhðasÞ @ ð5Þ R T For constant T, Eq. (5) can be rewritten into Eq. (6). 1 @ ln½sinhðasÞ ¼ n @ lne_
ð6Þ
In accordance with the relationship curves of ln[sinh(asp)] and ln e_ (Fig. 4a), the average value of n can be estimated to be 5.2035. According to Eq. (5), Eq. (7) can be obtained. Q ¼ Rn
@ ln½sinhðasÞ @ 1=T
ð7Þ
In accordance with the relationship curves of ln[sinh(asp)] and 1/T (Fig. 4b), the average value of the slopes is 7155.554. So the value of Q can be obtained as 309.583 kJ/mol using Eq. (7). Then A
Fig. 3. Relationships between strain rates and peak stresses: (a) ln e_ and sp; (b) ln e_ and ln sp.
can be easily obtained as 8.1264 1010. Finally, substituting the values of n, A and Q into Eq. (1) and Eq. (4), the peak stress constitutive equation of hot deformation for the experimental steel can be expressed as Eq. (8). Z ¼ e_ exp 309583=RT ¼ 8:1264 1010 ðsinh 0:01sp Þ5:2035 ð8Þ Q is an important material parameter serving as an indicator of deformation difficulty in hot deformation. There are some regression expressions corresponding to chemical composition to predict the Q value. One of the expressions to calculate the Q value of microalloyed steels was proposed by Medina and Hernandez [24], Q J=mol ¼ 2670002535:52ðC%Þ þ1010ðMn%Þ þ33620:76ðSi%Þ þ35651:28ðMo%Þ þ93680:52ðTi%Þ0:5919 þ 31673:46ðV%Þ þ70729:85ðNb%Þ0:5649
ð9Þ
where (%) depicts the total content of the given elements in the studied steel. Table 2 lists both the experimental activation energy Qexp and calculated activation energy Qcal by Eq. (9) of some microalloyed steels [15,24,25] and the experimental activation energy Qexp of some stainless steels [26–30], the a value in Eq. (4) is also listed in Table 2.
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Table 2 The a value and activation energy of some microalloyed steels and stainless steels obtained by compression or torsion testing.
a (M Pa 1)
Qexp (kJ/mol)
Qcal (kJ/mol)
DQ Q exp
0.2–50 s 1 0.2–50 s 1 0.2–50 s 1 0.001–0.5 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.5–6 s 1 0.01–30 s 1
0.012 0.012 0.012 0.0091 0.011875 0.011875 0.011875 0.011875 0.011875 0.01
312 325 326 320 285.2 294 296.5 287.8 294.5 310
284 297 297 305 285.3 293.8 296.7 287.8 294.5 302
8.97 8.62 8.89 4.69 0.035 0.068 0.068 0 0 2.58
0.0001–10 s 1 0.001–1 s 1 0.01–10 s 1 0.001–1 s 1 0.001–1 s 1
0.0105 0.012 0.00579 0.007 0.011
460 479 518 460 448
Materials
Test
Deforming condition
C–Mn–Ti C–Mn–Nb–Ti C–Mn–Nb–Ti–B C–Mn–V C–Mn–0.021Ti C–Mn–0.055Ti C–Mn–0.075Ti C–Mn–0.041Nb C–Mn–0.093Nb C–Mn–Nb–Ti–Al
Compression Compression Compression Compression Torsion Torsion Torsion Torsion Torsion Compression
800–1200 1C, 800–1200 1C, 800–1200 1C, 850–1100 1C, 900–1100 1C, 900–1100 1C, 900–1100 1C, 850–1100 1C, 850–1100 1C, 900–1100 1C,
PH stainless steel 2205 duplex stainless steel 316LN stainless steel PH stainless steel 410 martensitic stainless steel
Compression Compression Compression Compression Compression
900–1150 1C, 950–1200 1C, 900–1200 1C, 900–1100 1C, 900–1150 1C,
ð%Þ
Ref [25] [25] [25] [15] [24] [24] [24] [24] [24] This study [26] [27] [28] [29] [30]
The stress multiplier a is an adjustable constant which brings as into the correct range that gives linear and parallel lines in ln e_ vs. ln[sinh(as)]plots. It is found that the a values of microalloyed steels (including the experimental steel) listed in Table 2 are close to 0.012 M Pa 1, and the a values of stainless steels are in a wider range around 0.011 M Pa 1 (from 0.00579 to 0.012) in Table 2, which is in reasonable agreement with McQueen et al. [31] who indicated that the value of a had generally been 0.014 M Pa 1 for the HSLA steels and 0.012 M Pa 1 for stainless steels. The Q value of the experimental steel is close to that of austenite self-diffusion and equals well with Q values both in the creep and hot-working ranges [32–34], and it is also in reasonable agreement with that of microalloyed steels in the literature listed in Table 2. It seems that the high Al content in the experimental steel does not affect the activation energy much. On the other hand, the activation energy of stainless steels is much higher than that of microalloyed steels as seen in Table 2, which is due to the high solute content of Cr, Mo and Ni additions in stainless steels. At the same time, the calculated Qcal of the microalloyed steels is often lower than the measured value of Qexp as shown in Table 2. This is probably because some chemical elements such as Cr, Ni, B, Cu and Al in these steels were not considered in the Medina’s expression, which leads to the deviation between Qexp and Qcal. However, the relative error of all the calculated Q value in Table 2 is less than 10% (for the experimental steel, the relative error is 2.58%). It suggests that Eq. (9) can be applied to obtain a first approximation of Q values of microalloyed steels, if no better equation available.
3.3. DRX analysis Microstructures of the experimental steel deformed at different conditions to a strain of 1.0 are shown in Figs. 5 and 6. It can be seen from Fig. 5 that at the temperature of 900 1C and strain rate of 10 s 1, we can see that the original grains were elongated along the deformation direction. As the temperature increased to 950 1C, the original grains were elongated along the deformation direction, moreover, there are a few new fine grains were nucleated at the serrated part of initial grain boundaries, demonstrating occurrence of DRX. As the temperature increased to 1000 1C, more new fine DRX grains emerged at prior grain boundaries, and the necklace structure started to form, as seen in Fig. 5c. As the deformation temperature further increased to 1050 1C, the volume fraction of the recrystallized grains increased
Fig. 4. Relationship between (a) ln[sinh(asp)] and ln e_ ; (b) ln[sinh(asp)] and 1/T.
dramatically, and the majority of the original grains were replaced by new fine DRX grains. From Fig. 6, it can be seen that at the temperature of 1000 1C and strain rate of 30 s 1, the original grains were elongated along the deformation direction, a few new DRX grains were nucleated at the serrated part of initial grain boundaries, demonstrating occurrence of the DRX. As the strain rate decreased to 1 s 1, more
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Fig. 5. Optical deformed microstructures at a strain of 1.0 under different temperatures at 10 s 1: (a) 900 1C; (b) 950 1C; (c) 1000 1C and (d) 1050 1C.
Fig. 6. Optical deformed microstructures at a strain of 1.0 under different conditions: (a) 1000 1C, 30 s 1; (b) 1000 1C, 1 s 1; (c) 1000 1C, 0.1 s 1 and (d) 1100 1C, 0.01 s 1.
new fine DRX grains emerged at prior grain boundaries. As the strain rate decreased to 0.1 s 1, the volume fraction of the recrystallized grains increased dramatically, and the original grains were replaced completely by new fine DRX grains, the DRX process had been completed, as seen in Fig. 6c. Fig. 6d shows the microstructure of the specimen deformed at 1100 1C and 0.01 s 1. It can be seen that as the deformation temperature
increased to 1100 1C and the strain rate decreased to 0.01 s 1, the DRX grains coarsened obviously. From the analysis above, it is known that the DRX is dependent sensitively on the deformation temperature and strain rate in the experimental steel. Both effects of deformation temperature and strain rate on the DRX process can be summed up in Z parameter. Decreasing of Z value, that is increasing deformation temperature
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Fig. 7. Relationship between Ds and Z.
and/or decreasing strain rate, leads to more adequate proceeding of DRX. The previous researchers concluded that the steady state grain size is independent on the initial grain size and remains almost unchanged at strains over the onset of steady state flow [35,36]. In this research, the steady state grain size was measured under various deformation conditions and found that it decreased with the increase in strain rate and the decrease in temperature. To model the dependence of the steady state grain size on temperature and strain rate, the following relationship is used. Ds ¼ BZ k
ð10Þ
Fig. 7 and Eq. (11) show the relationship between the steady state grain size Ds and Zener–Hollomon parameter Z of the experimental steel. lnDs ¼ 0:2005 lnZ þ 7:2644
ð11Þ
The Zener–Hollomon exponent k¼0.2005 is within the scatter of those reported in the literature: 0.13 [37], 0.167 [38], 0.193 [39] and 0.27 [40] for microalloyed steels without high Al addition. The peak strain ep is an important parameter. The critical strain ec at which dynamic recrystallization begins can be approximately determined by the peak strain ep. Therefore, peak strain can be used to estimate whether the deformed austenite will dynamically recrystallize and what percentage of the volume has recrystallized [41]. For the experimental steel, ep is also dependent on Zener– Hollomon parameter Z according to Fig. 8(a) and Eq. (12). lnep ¼ 0:0995 lnZ3:4632
ð12Þ
The Zener–Hollomon exponent 0.0995 is close to those values in the range 0.12–0.22 reported by other workers for microalloyed steels and stainless steels [25,42]. For Nb steel and 17–4 PH stainless steel, the low values of 0.09 and 0.11 have also been reported [43,44]. At the same time, the relationship between sp and Z is also plotted (Fig. 8(b)) and a relationship is obtained in Eq. (13). lnsp ¼ 0:1459 lnZ þ 0:7984
ð13Þ
The Zener–Hollomon exponent 0.1459 is also close to previous reports such as 0.147 [14] and 0.14 [45]for microalloyed steels without high Al addition. From the analysis above, it can be seen that the values of those Zener–Hollomon exponents of the steady state grain size, the peak strain and the peak stress for the experimental steel were in reasonable agreement with other microalloyed steels without
Fig. 8. Relationship between (a) ep and Z; (b) sp and Z.
high Al addition, so it is inferred that the high Al addition in microalloyed steels may not affect much the values of those Zener–Hollomon exponents.
4. Conclusions (1) The flow stress constitutive equation of the experimental steel was developed. The activation energy of hot working is about 310 kJ/mol, which is in reasonable agreement with those reported before. (2) A regression expression proposed by Medina et al. to predict the Q value of microalloyed steel was found to have a relative error 2.58% for this steel, and can be used for first approximations. (3) Microstructure examination shows that DRX behavior of this steel is dependent sensitively on the deformation temperature and strain rate, increasing deformation temperature and/ or decreasing strain rate will lead to more adequate proceeding of DRX. (4) The steady state grain size of the experimental steel increases with the increase of temperature and decrease of the strain rate in the form of ln Ds ¼ 0.2005 ln Z þ7.2644. The Zener– Hollomon exponent 0.2005 is within the scatter of those reported for microalloyed steels without high Al addition. (5) For the experimental steel, the dependence of ep and sp on Zener–Hollomon parameter Z has the form of ln ep ¼0.0995
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ln Z 3.4632 and ln sp ¼0.1459 ln Zþ0.7984. The Zener– Hollomon exponents 0.0995 and 0.1459 are in agreement with values in the range reported by other workers for microalloyed steels without high Al addition.
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