- Email: [email protected]
Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
Journal of University of Science and Technology Beijing Volume 15, Number 4, August 2008, Page 396
Materials
Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels Yunbo Xu, Yongmei Yu, Xianghua Liu, and Guodong Wang State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, China (Received 2007-09-15)
Abstract: An integrated metallurgical model was developed for Nb steels to predict the microstructure evolution and mechanical properties during the hot-strip rolling and cooling process. On the basis of the industrial data, the transformation kinetics, strength, and elongation rate were evaluated for different chemical compositions and processing parameters. The yield strength and tensile strength increase with increasing Nb content or decreasing finishing temperature. The bainite distributed in finer ferrite matrix, which is produced at relatively low coiling temperatures, can greatly increase the strength of steel, especially tensile strength, thereby decreasing the yield ratio. A reasonable agreement was found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process. © 2008 University of Science and Technology Beijing. All rights reserved. Key words: hot-strip rolling; transformation; microstructure; mechanical properties; grain size
[This study was financially supported by the National Natural Science Foundation of China (No.50504007, No.50474086, and No.50334010).]
1. Introduction As already known, the mechanical properties of steels depend on their microstructures such as grain size, dislocation density, precipitates, second phase, and alloying elements. To improve the mechanical properties and reduce cost, computer simulation has been used to describe the microstructure evolution in rolling and cooling of steels. In the past two decades, some mathematical models [1-12] have been developed to gain a detailed knowledge of metallurgical phenomena in the thermomechanical process. These models, however, are mostly based on regression or mathematical statistics and are only applicable to the simulation for a given process. Therefore, it is necessary to adopt the theories of nucleation and growth and the thermodynamics in the formulation of metallurgical phenomenon. The present study aims to develop a metallurgical model capable of estimating the microstructure evolution and mechanical properties during hot-strip rolling and cooling in the steels microalloyed with Nb. Based Corresponding author: Yunbo Xu, E-mail: [email protected] © 2008 University of Science and Technology Beijing. All rights reserved.
on the metallurgical principle and industrial data, the transformation kinetics and tensile properties were computed for different chemical compositions and processing parameters. The present model can provide a complete understanding of metallurgical event during hot rolling, which has already been used successfully for on-line processing monitor and control.
2. Mathematical model The transformations from work-hardened austenite to ferrite, pearlite, and bainite are the major metallurgical phenomenon during continuous cooling of hot rolled strip. Based on the generalized Kolmogorov-Johnson-Mehl-Avrami (KJMA) type equation, Chan’s theory, and Scheil’s additivity rule [8-9], the transformation kinetics, such as ferrite nucleation and growth, transformed phase volume fraction, and grain size, are analyzed below. The final mechanical properties can be calculated by the relation equations between the microstructure and properties developed in this article. Also available online at www.sciencedirect.com
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
397
2.1. Mathematical formulation for isothermal phase transformation
chemical potential of austenite by deformation, 'P d ,
According to Cahn’s transformation kinetics theory, at the earlier stage of Ȗ»Į transformation, the transformation follows the nucleation-growth mechanism, and the kinetics equation is
'P d
1 exp( ʌI F S Ȗ G F3t 4 / 3)
XF
(1)
At the latter stage of ȖėĮ transformation, the kinetics equation is given according to the site-saturation mechanism as
is (6)
0.5PU b 2V Ȗ
where P and b are the shear modulus and Burger’s vector, respectively. U is the dislocation density, cm2, and the calculation method in Ref. [15] is adopted in this article, V Ȗ the molar volume of austenite.
where X F is the transformed ferrite fraction, t the isothermal holding time, S Ȗ the effective boundary area, I F the nucleation rate, and G F the grain growth rate.
The effect of deformation is not considered in the nucleation rate model proposed by Aaronson [10], and therefore, it is available only for undeformed or recrystallized austenite. Here, the nucleation driving force, 'G F , is adopted instead of the free energy change under undeformed condition, 'G V , 'G F 'G V 'P d . At the same time, the deformation coefficient, \ exp(O 'H ) , is introduced to de-
Pearlite and bainite transformations can be represented by similar equations assuming that they proceed after the saturation of nucleation site, where, G P(B) is the growth rate of pearlite (bainite), which is calculated by the method referred in Ref. [13].
scribe the effect of the effective deformation ledge on nucleation energy, where 'H is the residue strain, and O the constant used to fit the measured data and predictions. The nucleation rate I F and the grain growth rate G F can be described by the following equations.
XF
1 exp(2S Ȗ G F t )
X P(B)
1 exp(2 S Ȗ G P(B) t )
(2)
(3)
IF
The total number of D nuclei at the early stage of transformation ( n F ) is nF
tc
I F (1 X F )dt
³0
(4)
where t c is the transition time of mechanism [14]. Assuming that D grain is spherical, the average grain size ( d F ) is dF
(6 X F / ʌn F S Ȗ )1 / 3
(5)
2.2. Influence of deformation on phase transformation The effect of deformation on the transformation kinetics is mainly considered from three aspects: (1) the change in free energy; (2) the change in nucleation rate; (3) the change in the boundary area for nucleation. Deformation will raise the free energy of austenite, move up the free energy-composition curve, and therefore, change the equilibrium phase composition and transformation driving force. The increment of the q
S Ȗd
2ʌ ³
1/(1 p )
0
(1 p ) / 1 (1 p ) 2 x 2
³0
A[ ln(1 p )] 2 6q / d Ȗ
ª (1 p ) 4 x 2 y 2 /(1 p ) 4 º «1 2 2 2 2» ¬ 1 (1 p ) x y /(1 p ) ¼
(10)
where p is the reduction rate, dJ the final austenite grain size, A the constant, and q the ratio of austenite grain boundary area after and before deformation.
ª \ (H ) K 2 I 3 ([Mn]% ,[Nb]%) º K 1D C exp « » 1/ 2 (kT ) RT ('G F ) 2 ¬ ¼
(7a) a1 a 2 [Mn]% a 3 [Nb]% (1 f p )
I GF
x Ȗ/Ȗ+Į x CȖ 1 DC CȖ 4r0 x C x CĮ/Į+Ȗ
(7b) (8)
where K 1 , K 2 , and ai (i=1-3) are material dependent constants and their values are obtained from the analysis of the experiment data. Dc is the C diffuse coefficient in austenite, fp the precipitated fraction of Nb(CN), R the gas constant, x C0 the original C element content, and r0 the ferritic ultimate radius of curvature. The increase in ferrite nucleation rate per unit volume of austenite by work-hardening is mainly attributed to (1) the increase in austenite grain surface area by the elongation of grains and (2) the formation of additional nucleation site such as annealing twin boundaries and deformation band. Thus, the effective boundary area S Ȗ should be replaced by S Ȗd : 1/ 2
dxdy
(9)
2.3. Incremental phase transformation model under continuous cooling Scheil’s additivity rule is adopted to treat austenite transformation during continuous cooling, that is,
398
J. Univ. Sci. Technol. Beijing, Vol.15, No.4, Aug 2008
treating this transformation as a sum of little isothermal processes. This transformation start temperature is achieved when the following equation is satisfied: 't i
f
¦ Wi
(11)
1
i
where 't i is the slight increment of time, W i the incubation time of transformation at different temperatures. Austenite to ferrite, pearlite, and bainite transformations satisfy or approximately satisfy the additivity rule, that is: X nj
(12)
X nj1 'X nj
where X represents the transformed volume fraction of each phase, and j represents each phase. 2.4. Mechanical property model The important mechanical properties of steel strips such as tensile strength (TS), yield strength (YS), and elongation rate (Er) are formulated with the calculated microstructure and transformation kinetics parameters. The equations for the prediction of YS are described as:
u[X F (H F vd F1/2 ) X P H P X B H B ] w
(14)
where HF, HP, and HB indicate the microhardness of ferrite, pearlite, and bainite respectively, and u, v, and w are constants. The elongation rate is formulated by (15)
G = G 0 +vH F X F + yH P X P +zH B X B +md Fˉ1/2
where v, y, z, and m are constants, and G0 is a parameter associated with the finished thickness and finishing temperature.
3. Simulation results The industrial rolling data were obtained from a hot strip mill for different steels. The strip rolling line layout is shown in Fig. 1. The composition (wt%) of the material is C, 0.09; Mn, 1.45; Si, 0.22; and Nb, 0.02. The size of the continuous casting blank was 260 mmu1520 mmu10400 mm and the reheating temperature was 1213qC. After 6-pass roughing and 7-pass finishing, the slab was cooled down at some rates and subsequently coiled at a reasonable temperature.
(13b)
V disl D M PbU 1 2 V ppt
Vb
(13a)
V 0 V disl V ppt pd F1/2
Vs
method as shown in the following equation:
6P bf p1/ 2 § S k dd p · u ln ¨ ¸ 3/ 2 1.18ʌ k p d p © 4b ¹
(13c)
where V 0 is the base strength associated with solution hardening, V s the yield strength, V disl the stress increment by the increase in dislocation, V ppt the precipitation strengthening, M the Taylor factor, d p and f p indicate the precipitated particle size and fraction [16], respectively, and D, k p , k d , p are constants.
Fig. 1. mill.
Schematic diagram of the rolling line of a hot strip
Fig. 2 shows the influence of finishing temperature (Fig. 2(a)), finishing total reduction ratio (Fig. 2(b)), and Nb content (Fig. 2(c)) on the mechanical properties during hot strip rolling of Nb steels. The finishing reduction schedule in Fig. 2(a) is shown in Table 1, and the finishing temperature of 840qC is adopted in Figs. 2(b) and (c).
Tensile strength is predicted by the strain partition Table 1. Rolling pass
Process parameters adopted during hot rolling of an 8-mm plate Roughing 1
h0 / mm
h1 / mm
vr / (ms )
R1 R2 R3 R4 R5
220 180 140 106 81
180 140 106 81 62
0.97 1.41 1.90 2.49 3.18
R6 R7
62
49
3.75
As seen in Fig. 2(a), the yield strength and tensile strength increase with decreasing finishing tempera-
Rolling pass
Finishing h0 / mm
h1 / mm
vr / (ms1)
F1 F2 F3 F4 F5
49 33 23 17 13
33 23 17 13 10
0.97 1.41 1.90 2.49 3.18
F6 F7
10 9
9 8
3.75 4.30
ture and there is no evident variation in elongation rate. For the steel studied, the change of yield strength is in
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
the range of 50 MPa and that of tensile strength is less than 20 MPa. The refinement of ferrite grain owing to the low finishing temperatures is the most important reason for this variation of properties. At low finishing temperatures, work-hardened austenite contains various kinds of defects such as dislocations, deformation bands, and deformed annealing twins, which are the possible nucleation sites of ferrite in addition to the elongated grain boundary of austenite On the other hand, the fine austenite grain produced at low finishing temperatures can also cause the sharp increase of ferrite nucleation site. Therefore, the ferrite transformation kinetics is enhanced and the final microstructure is refined. Additionally, the decrease in finishing temperature also promotes the formation of pearlite instead of little bainite produced at high finishing temperatures. This is because the accelerated ferrite transition increases the carbon content in the austenite matrix and thus leads to preferential precipitation of cementite. Noting that, the elongation rate is associated with the microstructure characteristics of the material and thus its change does not show obvious trend.
399
addition, the high Nb content is available to magnify the precipitation strengthening of the fine carbonitride formed in the ferrite matrix. It is well known that coiling temperature, finishing temperature, and load distribution are the most critical parameters during hot rolling, which will determine the final grain size and the mechanical properties. Fig. 3 describes the influence of coiling temperature on the mechanical properties (Fig. 3(a)) and the transformed microstructure (Fig. 3(b)). Here, the finished thickness is 8 mm and the finishing temperature is about 840qC.
It is seen from Fig. 2(b) that the yield strength, tensile strength, and elongation rate increase with increasing total reduction ratio in finishing. The reason is similar to the one in Fig. 2(a), and the difference is that the grain refinement effect of the latter is more significant. Here, firstly, the austenite grain is to be discussed. The high total deformation amount and the small softening fraction at low temperatures possibly lead to the occurrence of dynamic and metadynamic recrystallization, thus further refining austenite grains. In the present case, austenite grains can be refined to about 12 Pm. Therefore, when the finishing temperature is 840qC and the total reduction ratio is about 96%, the ferrite grain size will reach about 5 Pm and the yield strength will increase to about 486 MPa. The strong refinement results in not only high strength but also good plasticity, and thereby, high elongation rate is obtained when the total reduction ratio is large enough. Similarly, bainite cannot be observed at a high total reduction amount. It must be noted that when bainite is absent, the ferrite grain refinement results in an increase in yield ratio, which is not expected. The influence of Nb content on the tensile properties is shown in Fig. 2(c). The yield and tensile strengths increase with increasing Nb content and there is no large change for the elongation rate. The Nb additions play an important role in delaying recrystallization, elongating austenite grains, and increasing residual strain, which result in ferrite grain refinement during the subsequent transformation. In
Fig.2. Variations of properties with the finishing temperature (a), finishing total reduction ratio (b), and Nb content (c).
The yield strength and tensile strength rapidly increase with decreasing coiling temperature, especially at low coiling temperatures. This is mainly because coiling temperature has a significant influence on not only ferrite grain size but also transformed volume
400
J. Univ. Sci. Technol. Beijing, Vol.15, No.4, Aug 2008
fraction. When the coiling temperature ranges from 450 to 780qC, the ferrite grain size changes between 6 to 10 Pm and the variation of yield strength is close to 60 MPa. At low coiling temperatures, that is to say, at high cooling rates, the undercooling degree and the ferrite nucleation driving force increase, and the nucleation rate is quickly raised, and thereby ferrite grains are further refined. For the ferrite+pearlite type steels, the increment of yield strength owing to grain refinement is considerably greater than that of tensile strength and thus the yield ratio is raised, which is not good for the combination property of the studied steel. It is however seen from Fig. 3(b) that the ferrite fraction decreases with decreasing coiling temperature and bainite can be obtained when the coiling temperature is lower than 600qC and its amount quickly increases with decreasing coiling temperature. The bainite dis-
tributed in fine ferrite base can increase the strength of the microstructure, especially the tensile strength, therefore decreasing yield ratio. It is noticed that the effect of coiling temperature on the properties is considered to be associated with finishing temperature, which is more significant at relatively low coiling temperatures, owing to the incomplete softening and strong work-hardening. Fig. 4 shows the comparison of the predicted and measured volume fractions of transformed phases and strengths. A reasonable agreement is found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process. The chemical composition and key processing parameters adopted in this case are shown in Tables 2 and 3.
Fig. 3. Variations of the mechanical properties and transformed microstructure with coiling temperature: (a) mechanical properties; (b) transformed volume fraction and grain size.
Fig. 4. Comparison of the predicted and measured microstructures and properties: (a) volume fraction of transformed phases; (b) strength. Table 2.
Chemical composition of the studied materials (Nb steel)
wt%
C
Mn
Si
S
P
Nb
0.01-0.20
0.2-1.8
0.01-1.4
0.020
0.020
0.004-0.05
Table 3.
Hot-strip rolling parameters used in this article
Reheating temperature / qC
Finishing temperature /qC
Coiling temperature /qC
Thickness / mm
Width / mm
1150-1250
780-950
440-750
2-16
600-1800
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
4. Conclusions (1) The yield and tensile strengths increase with decreasing finishing temperature or increasing total reduction ratio in finishing or increasing Nb content. When the finishing temperature is 840qC and the total reduction ratio is about 96%, the ferrite grain size will reach about 5 Pm and the yield strength will increase to about 486 MPa, and the increment of yield strength owing to grain refinement is considerably greater than that of tensile strength for the ferrite+pearlite type steels. (2) Coiling temperature has a more significant effect on strength in comparison with finishing temperature and finishing total reduction ratio. When the coiling temperature ranges from 450 to 780qC, the ferrite grain size changes between 6 and 10 Pm and the variation in yield strength is close to 60 MPa. The bainite obtained at relatively low coiling temperatures can increase the strength of the steel, especially tensile strength, thereby decreasing the yield ratio. (3) A reasonable agreement was found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process.
References [1] M. Gqmez, S.F. Medina, and P. Valles, Determination of driving and pining forces for static recrystallization during hot rolling of a niobium microalloyed steel, ISIJ Int., 45(2005), No.11, p.1711. [2] J.S. Liu, A. Yanagida, and S. Sugiyama, The analysis of phase transformation for the prediction of microstructure change after hot forming, ISIJ Int., 41(2001), No.12, p.1510. [3] M. Militzer, E.B. Hawbolt, and T.R. Meadowcroft, Microstructure model for hot strip rolling of high-strength low-alloy steel, Metall. Mater. Trans. A, 31(2000), No.12, p.1247.
401
[4] M. Militzer, R. Pandi, and E.B. Hawbolt, Ferrite nucleation and growth during continuous cooling, Metall. Mater. Trans. A, 27(1996), No.7, p1547. [5] T.M. Maccagon, J.J. Jonas, and P.D. Hodgson, Spreadsheet modeling of grain size evolution during rod rolling, ISIJ Int., 36(1996), No.6, p.720. [6] K.J. Lee, K.B. Kang, and O. Kwon, Mathematical modeling of transformation in Nb microalloyed steels, ISIJ Int., 32(1992), No.3, p.326. [7] K. Minami, J.F. Siciliano, T.M. Maccagno, et al., Mathematical modeling of mean flow stress during the hot strip rolling of Nb steels. ISIJ Int., 36(1996), No.3, p.1507. [8] J.W. Cahn, The kinetics of grain boundary nucleated reaction, Acta Metall., 4(1956), p.449. [9] T.T. Pham, E.B. Hawbolt, and J.K. Brimacombe, Predicting the onset of transformation under noncontinuous cooling conditions, Metall. Mater. Trans. A, 26(1995), p.1987. [10] E.B. Hawbolt, B. Chau, and J.K. Brimacombe, Kinetics of austenite-ferrite and austenite-pearlite transformation in a 1025 carbon steel, Metall. Trans. A, 16(1985), No.4, p.565. [11] D.N. Hanlon, J. Sietsma, and S.V. Zwaag, The effect of plastic deformation of austenite on the kinetics of subsequent ferrite formation, ISIJ Int., 41(2001), No.9, p.1028. [12] M. Enomoto and H.I. Aaronson, Nucleation kinetics of proeutectoid ferrite at austenite grain boundaries in Fe-C-X alloys, Metall. Trans. A, 17(1986), No.9, p.1385. [13] J.B. Qu, Z.D. Wang, X.H. Liu, et al., Modelling of prediction of continuous cooling transformation kinetics of hot-deformed austenite steel, Acta Metall. Sin. (Engl. Ed.), 11(1998), No.3, p.225. [14] J.B. Qu, Predicting and Controlling the Microstructure and Property of Hot Rolled HSLA Steel Plate [Dissertation], Northeastern University, Shenyang, 1998. [15] B. Dutta, E.J. Palmiere, and C.M. Sellars, Modeling the kinetics of strain induced precipitation in Nb microalloyed steels, Acta. Mater., 49(2001), p.785. [16] Y.B. Xu, Y.M. Yu, X.H. Liu, and G.D. Wang, Mathematical modeling of carbonitride precipitation during hot working in Nb microalloyed steels, J. Mater. Sci. Technol., 22(2006), No.2, p.149.
Materials
Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels Yunbo Xu, Yongmei Yu, Xianghua Liu, and Guodong Wang State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, China (Received 2007-09-15)
Abstract: An integrated metallurgical model was developed for Nb steels to predict the microstructure evolution and mechanical properties during the hot-strip rolling and cooling process. On the basis of the industrial data, the transformation kinetics, strength, and elongation rate were evaluated for different chemical compositions and processing parameters. The yield strength and tensile strength increase with increasing Nb content or decreasing finishing temperature. The bainite distributed in finer ferrite matrix, which is produced at relatively low coiling temperatures, can greatly increase the strength of steel, especially tensile strength, thereby decreasing the yield ratio. A reasonable agreement was found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process. © 2008 University of Science and Technology Beijing. All rights reserved. Key words: hot-strip rolling; transformation; microstructure; mechanical properties; grain size
[This study was financially supported by the National Natural Science Foundation of China (No.50504007, No.50474086, and No.50334010).]
1. Introduction As already known, the mechanical properties of steels depend on their microstructures such as grain size, dislocation density, precipitates, second phase, and alloying elements. To improve the mechanical properties and reduce cost, computer simulation has been used to describe the microstructure evolution in rolling and cooling of steels. In the past two decades, some mathematical models [1-12] have been developed to gain a detailed knowledge of metallurgical phenomena in the thermomechanical process. These models, however, are mostly based on regression or mathematical statistics and are only applicable to the simulation for a given process. Therefore, it is necessary to adopt the theories of nucleation and growth and the thermodynamics in the formulation of metallurgical phenomenon. The present study aims to develop a metallurgical model capable of estimating the microstructure evolution and mechanical properties during hot-strip rolling and cooling in the steels microalloyed with Nb. Based Corresponding author: Yunbo Xu, E-mail: [email protected] © 2008 University of Science and Technology Beijing. All rights reserved.
on the metallurgical principle and industrial data, the transformation kinetics and tensile properties were computed for different chemical compositions and processing parameters. The present model can provide a complete understanding of metallurgical event during hot rolling, which has already been used successfully for on-line processing monitor and control.
2. Mathematical model The transformations from work-hardened austenite to ferrite, pearlite, and bainite are the major metallurgical phenomenon during continuous cooling of hot rolled strip. Based on the generalized Kolmogorov-Johnson-Mehl-Avrami (KJMA) type equation, Chan’s theory, and Scheil’s additivity rule [8-9], the transformation kinetics, such as ferrite nucleation and growth, transformed phase volume fraction, and grain size, are analyzed below. The final mechanical properties can be calculated by the relation equations between the microstructure and properties developed in this article. Also available online at www.sciencedirect.com
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
397
2.1. Mathematical formulation for isothermal phase transformation
chemical potential of austenite by deformation, 'P d ,
According to Cahn’s transformation kinetics theory, at the earlier stage of Ȗ»Į transformation, the transformation follows the nucleation-growth mechanism, and the kinetics equation is
'P d
1 exp( ʌI F S Ȗ G F3t 4 / 3)
XF
(1)
At the latter stage of ȖėĮ transformation, the kinetics equation is given according to the site-saturation mechanism as
is (6)
0.5PU b 2V Ȗ
where P and b are the shear modulus and Burger’s vector, respectively. U is the dislocation density, cm2, and the calculation method in Ref. [15] is adopted in this article, V Ȗ the molar volume of austenite.
where X F is the transformed ferrite fraction, t the isothermal holding time, S Ȗ the effective boundary area, I F the nucleation rate, and G F the grain growth rate.
The effect of deformation is not considered in the nucleation rate model proposed by Aaronson [10], and therefore, it is available only for undeformed or recrystallized austenite. Here, the nucleation driving force, 'G F , is adopted instead of the free energy change under undeformed condition, 'G V , 'G F 'G V 'P d . At the same time, the deformation coefficient, \ exp(O 'H ) , is introduced to de-
Pearlite and bainite transformations can be represented by similar equations assuming that they proceed after the saturation of nucleation site, where, G P(B) is the growth rate of pearlite (bainite), which is calculated by the method referred in Ref. [13].
scribe the effect of the effective deformation ledge on nucleation energy, where 'H is the residue strain, and O the constant used to fit the measured data and predictions. The nucleation rate I F and the grain growth rate G F can be described by the following equations.
XF
1 exp(2S Ȗ G F t )
X P(B)
1 exp(2 S Ȗ G P(B) t )
(2)
(3)
IF
The total number of D nuclei at the early stage of transformation ( n F ) is nF
tc
I F (1 X F )dt
³0
(4)
where t c is the transition time of mechanism [14]. Assuming that D grain is spherical, the average grain size ( d F ) is dF
(6 X F / ʌn F S Ȗ )1 / 3
(5)
2.2. Influence of deformation on phase transformation The effect of deformation on the transformation kinetics is mainly considered from three aspects: (1) the change in free energy; (2) the change in nucleation rate; (3) the change in the boundary area for nucleation. Deformation will raise the free energy of austenite, move up the free energy-composition curve, and therefore, change the equilibrium phase composition and transformation driving force. The increment of the q
S Ȗd
2ʌ ³
1/(1 p )
0
(1 p ) / 1 (1 p ) 2 x 2
³0
A[ ln(1 p )] 2 6q / d Ȗ
ª (1 p ) 4 x 2 y 2 /(1 p ) 4 º «1 2 2 2 2» ¬ 1 (1 p ) x y /(1 p ) ¼
(10)
where p is the reduction rate, dJ the final austenite grain size, A the constant, and q the ratio of austenite grain boundary area after and before deformation.
ª \ (H ) K 2 I 3 ([Mn]% ,[Nb]%) º K 1D C exp « » 1/ 2 (kT ) RT ('G F ) 2 ¬ ¼
(7a) a1 a 2 [Mn]% a 3 [Nb]% (1 f p )
I GF
x Ȗ/Ȗ+Į x CȖ 1 DC CȖ 4r0 x C x CĮ/Į+Ȗ
(7b) (8)
where K 1 , K 2 , and ai (i=1-3) are material dependent constants and their values are obtained from the analysis of the experiment data. Dc is the C diffuse coefficient in austenite, fp the precipitated fraction of Nb(CN), R the gas constant, x C0 the original C element content, and r0 the ferritic ultimate radius of curvature. The increase in ferrite nucleation rate per unit volume of austenite by work-hardening is mainly attributed to (1) the increase in austenite grain surface area by the elongation of grains and (2) the formation of additional nucleation site such as annealing twin boundaries and deformation band. Thus, the effective boundary area S Ȗ should be replaced by S Ȗd : 1/ 2
dxdy
(9)
2.3. Incremental phase transformation model under continuous cooling Scheil’s additivity rule is adopted to treat austenite transformation during continuous cooling, that is,
398
J. Univ. Sci. Technol. Beijing, Vol.15, No.4, Aug 2008
treating this transformation as a sum of little isothermal processes. This transformation start temperature is achieved when the following equation is satisfied: 't i
f
¦ Wi
(11)
1
i
where 't i is the slight increment of time, W i the incubation time of transformation at different temperatures. Austenite to ferrite, pearlite, and bainite transformations satisfy or approximately satisfy the additivity rule, that is: X nj
(12)
X nj1 'X nj
where X represents the transformed volume fraction of each phase, and j represents each phase. 2.4. Mechanical property model The important mechanical properties of steel strips such as tensile strength (TS), yield strength (YS), and elongation rate (Er) are formulated with the calculated microstructure and transformation kinetics parameters. The equations for the prediction of YS are described as:
u[X F (H F vd F1/2 ) X P H P X B H B ] w
(14)
where HF, HP, and HB indicate the microhardness of ferrite, pearlite, and bainite respectively, and u, v, and w are constants. The elongation rate is formulated by (15)
G = G 0 +vH F X F + yH P X P +zH B X B +md Fˉ1/2
where v, y, z, and m are constants, and G0 is a parameter associated with the finished thickness and finishing temperature.
3. Simulation results The industrial rolling data were obtained from a hot strip mill for different steels. The strip rolling line layout is shown in Fig. 1. The composition (wt%) of the material is C, 0.09; Mn, 1.45; Si, 0.22; and Nb, 0.02. The size of the continuous casting blank was 260 mmu1520 mmu10400 mm and the reheating temperature was 1213qC. After 6-pass roughing and 7-pass finishing, the slab was cooled down at some rates and subsequently coiled at a reasonable temperature.
(13b)
V disl D M PbU 1 2 V ppt
Vb
(13a)
V 0 V disl V ppt pd F1/2
Vs
method as shown in the following equation:
6P bf p1/ 2 § S k dd p · u ln ¨ ¸ 3/ 2 1.18ʌ k p d p © 4b ¹
(13c)
where V 0 is the base strength associated with solution hardening, V s the yield strength, V disl the stress increment by the increase in dislocation, V ppt the precipitation strengthening, M the Taylor factor, d p and f p indicate the precipitated particle size and fraction [16], respectively, and D, k p , k d , p are constants.
Fig. 1. mill.
Schematic diagram of the rolling line of a hot strip
Fig. 2 shows the influence of finishing temperature (Fig. 2(a)), finishing total reduction ratio (Fig. 2(b)), and Nb content (Fig. 2(c)) on the mechanical properties during hot strip rolling of Nb steels. The finishing reduction schedule in Fig. 2(a) is shown in Table 1, and the finishing temperature of 840qC is adopted in Figs. 2(b) and (c).
Tensile strength is predicted by the strain partition Table 1. Rolling pass
Process parameters adopted during hot rolling of an 8-mm plate Roughing 1
h0 / mm
h1 / mm
vr / (ms )
R1 R2 R3 R4 R5
220 180 140 106 81
180 140 106 81 62
0.97 1.41 1.90 2.49 3.18
R6 R7
62
49
3.75
As seen in Fig. 2(a), the yield strength and tensile strength increase with decreasing finishing tempera-
Rolling pass
Finishing h0 / mm
h1 / mm
vr / (ms1)
F1 F2 F3 F4 F5
49 33 23 17 13
33 23 17 13 10
0.97 1.41 1.90 2.49 3.18
F6 F7
10 9
9 8
3.75 4.30
ture and there is no evident variation in elongation rate. For the steel studied, the change of yield strength is in
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
the range of 50 MPa and that of tensile strength is less than 20 MPa. The refinement of ferrite grain owing to the low finishing temperatures is the most important reason for this variation of properties. At low finishing temperatures, work-hardened austenite contains various kinds of defects such as dislocations, deformation bands, and deformed annealing twins, which are the possible nucleation sites of ferrite in addition to the elongated grain boundary of austenite On the other hand, the fine austenite grain produced at low finishing temperatures can also cause the sharp increase of ferrite nucleation site. Therefore, the ferrite transformation kinetics is enhanced and the final microstructure is refined. Additionally, the decrease in finishing temperature also promotes the formation of pearlite instead of little bainite produced at high finishing temperatures. This is because the accelerated ferrite transition increases the carbon content in the austenite matrix and thus leads to preferential precipitation of cementite. Noting that, the elongation rate is associated with the microstructure characteristics of the material and thus its change does not show obvious trend.
399
addition, the high Nb content is available to magnify the precipitation strengthening of the fine carbonitride formed in the ferrite matrix. It is well known that coiling temperature, finishing temperature, and load distribution are the most critical parameters during hot rolling, which will determine the final grain size and the mechanical properties. Fig. 3 describes the influence of coiling temperature on the mechanical properties (Fig. 3(a)) and the transformed microstructure (Fig. 3(b)). Here, the finished thickness is 8 mm and the finishing temperature is about 840qC.
It is seen from Fig. 2(b) that the yield strength, tensile strength, and elongation rate increase with increasing total reduction ratio in finishing. The reason is similar to the one in Fig. 2(a), and the difference is that the grain refinement effect of the latter is more significant. Here, firstly, the austenite grain is to be discussed. The high total deformation amount and the small softening fraction at low temperatures possibly lead to the occurrence of dynamic and metadynamic recrystallization, thus further refining austenite grains. In the present case, austenite grains can be refined to about 12 Pm. Therefore, when the finishing temperature is 840qC and the total reduction ratio is about 96%, the ferrite grain size will reach about 5 Pm and the yield strength will increase to about 486 MPa. The strong refinement results in not only high strength but also good plasticity, and thereby, high elongation rate is obtained when the total reduction ratio is large enough. Similarly, bainite cannot be observed at a high total reduction amount. It must be noted that when bainite is absent, the ferrite grain refinement results in an increase in yield ratio, which is not expected. The influence of Nb content on the tensile properties is shown in Fig. 2(c). The yield and tensile strengths increase with increasing Nb content and there is no large change for the elongation rate. The Nb additions play an important role in delaying recrystallization, elongating austenite grains, and increasing residual strain, which result in ferrite grain refinement during the subsequent transformation. In
Fig.2. Variations of properties with the finishing temperature (a), finishing total reduction ratio (b), and Nb content (c).
The yield strength and tensile strength rapidly increase with decreasing coiling temperature, especially at low coiling temperatures. This is mainly because coiling temperature has a significant influence on not only ferrite grain size but also transformed volume
400
J. Univ. Sci. Technol. Beijing, Vol.15, No.4, Aug 2008
fraction. When the coiling temperature ranges from 450 to 780qC, the ferrite grain size changes between 6 to 10 Pm and the variation of yield strength is close to 60 MPa. At low coiling temperatures, that is to say, at high cooling rates, the undercooling degree and the ferrite nucleation driving force increase, and the nucleation rate is quickly raised, and thereby ferrite grains are further refined. For the ferrite+pearlite type steels, the increment of yield strength owing to grain refinement is considerably greater than that of tensile strength and thus the yield ratio is raised, which is not good for the combination property of the studied steel. It is however seen from Fig. 3(b) that the ferrite fraction decreases with decreasing coiling temperature and bainite can be obtained when the coiling temperature is lower than 600qC and its amount quickly increases with decreasing coiling temperature. The bainite dis-
tributed in fine ferrite base can increase the strength of the microstructure, especially the tensile strength, therefore decreasing yield ratio. It is noticed that the effect of coiling temperature on the properties is considered to be associated with finishing temperature, which is more significant at relatively low coiling temperatures, owing to the incomplete softening and strong work-hardening. Fig. 4 shows the comparison of the predicted and measured volume fractions of transformed phases and strengths. A reasonable agreement is found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process. The chemical composition and key processing parameters adopted in this case are shown in Tables 2 and 3.
Fig. 3. Variations of the mechanical properties and transformed microstructure with coiling temperature: (a) mechanical properties; (b) transformed volume fraction and grain size.
Fig. 4. Comparison of the predicted and measured microstructures and properties: (a) volume fraction of transformed phases; (b) strength. Table 2.
Chemical composition of the studied materials (Nb steel)
wt%
C
Mn
Si
S
P
Nb
0.01-0.20
0.2-1.8
0.01-1.4
0.020
0.020
0.004-0.05
Table 3.
Hot-strip rolling parameters used in this article
Reheating temperature / qC
Finishing temperature /qC
Coiling temperature /qC
Thickness / mm
Width / mm
1150-1250
780-950
440-750
2-16
600-1800
Y.B. Xu et al., Modeling of microstructure evolution and mechanical properties during hot-strip rolling of Nb steels
4. Conclusions (1) The yield and tensile strengths increase with decreasing finishing temperature or increasing total reduction ratio in finishing or increasing Nb content. When the finishing temperature is 840qC and the total reduction ratio is about 96%, the ferrite grain size will reach about 5 Pm and the yield strength will increase to about 486 MPa, and the increment of yield strength owing to grain refinement is considerably greater than that of tensile strength for the ferrite+pearlite type steels. (2) Coiling temperature has a more significant effect on strength in comparison with finishing temperature and finishing total reduction ratio. When the coiling temperature ranges from 450 to 780qC, the ferrite grain size changes between 6 and 10 Pm and the variation in yield strength is close to 60 MPa. The bainite obtained at relatively low coiling temperatures can increase the strength of the steel, especially tensile strength, thereby decreasing the yield ratio. (3) A reasonable agreement was found between the predicted and measured results. It indicates that the present models can be used to simulate the actual production process.
References [1] M. Gqmez, S.F. Medina, and P. Valles, Determination of driving and pining forces for static recrystallization during hot rolling of a niobium microalloyed steel, ISIJ Int., 45(2005), No.11, p.1711. [2] J.S. Liu, A. Yanagida, and S. Sugiyama, The analysis of phase transformation for the prediction of microstructure change after hot forming, ISIJ Int., 41(2001), No.12, p.1510. [3] M. Militzer, E.B. Hawbolt, and T.R. Meadowcroft, Microstructure model for hot strip rolling of high-strength low-alloy steel, Metall. Mater. Trans. A, 31(2000), No.12, p.1247.
401
[4] M. Militzer, R. Pandi, and E.B. Hawbolt, Ferrite nucleation and growth during continuous cooling, Metall. Mater. Trans. A, 27(1996), No.7, p1547. [5] T.M. Maccagon, J.J. Jonas, and P.D. Hodgson, Spreadsheet modeling of grain size evolution during rod rolling, ISIJ Int., 36(1996), No.6, p.720. [6] K.J. Lee, K.B. Kang, and O. Kwon, Mathematical modeling of transformation in Nb microalloyed steels, ISIJ Int., 32(1992), No.3, p.326. [7] K. Minami, J.F. Siciliano, T.M. Maccagno, et al., Mathematical modeling of mean flow stress during the hot strip rolling of Nb steels. ISIJ Int., 36(1996), No.3, p.1507. [8] J.W. Cahn, The kinetics of grain boundary nucleated reaction, Acta Metall., 4(1956), p.449. [9] T.T. Pham, E.B. Hawbolt, and J.K. Brimacombe, Predicting the onset of transformation under noncontinuous cooling conditions, Metall. Mater. Trans. A, 26(1995), p.1987. [10] E.B. Hawbolt, B. Chau, and J.K. Brimacombe, Kinetics of austenite-ferrite and austenite-pearlite transformation in a 1025 carbon steel, Metall. Trans. A, 16(1985), No.4, p.565. [11] D.N. Hanlon, J. Sietsma, and S.V. Zwaag, The effect of plastic deformation of austenite on the kinetics of subsequent ferrite formation, ISIJ Int., 41(2001), No.9, p.1028. [12] M. Enomoto and H.I. Aaronson, Nucleation kinetics of proeutectoid ferrite at austenite grain boundaries in Fe-C-X alloys, Metall. Trans. A, 17(1986), No.9, p.1385. [13] J.B. Qu, Z.D. Wang, X.H. Liu, et al., Modelling of prediction of continuous cooling transformation kinetics of hot-deformed austenite steel, Acta Metall. Sin. (Engl. Ed.), 11(1998), No.3, p.225. [14] J.B. Qu, Predicting and Controlling the Microstructure and Property of Hot Rolled HSLA Steel Plate [Dissertation], Northeastern University, Shenyang, 1998. [15] B. Dutta, E.J. Palmiere, and C.M. Sellars, Modeling the kinetics of strain induced precipitation in Nb microalloyed steels, Acta. Mater., 49(2001), p.785. [16] Y.B. Xu, Y.M. Yu, X.H. Liu, and G.D. Wang, Mathematical modeling of carbonitride precipitation during hot working in Nb microalloyed steels, J. Mater. Sci. Technol., 22(2006), No.2, p.149.