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Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Available online at www.sciencedirect.com *-e0
Y0ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNPLIIONAL. 2008, 15(4) : 42-50
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process LI Xue-tong ,
WANG Min-ting ,
DU Feng-shan
(College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China)
Abstract: Using three-dimensional rigid-viscoplastic finite element method (FEM) , a coupling multivariable numerical simulation model for steel plate rolling has been established based on the physical metallurgy microstructural evolution rule and experiential equations. The effects of reduction, deformation temperature, and rolling speed on the deformation parameters and microstructure in plate rolling were investigated using the model. After a typical rolling process of steel plate 16Mn is simulated, the strain, temperature, and microstructure distributions are presented, as well as the ferrite grain transformation during the period of cooling. By comparing the calculated ferrite grain sizes with measured ones, the model is validated. Key words: hot rolling; plate; FEMi microstructure; coupling
A large variety of plates, as important iron and steel materials, are widely applied to shipbuilding, petrochemical industry, machine manufacturing, and so onC1’. In hot plate rolling, one side is to perform thickness reduction, and the other is to achieve grain refinement of austenite, which generally causes good complex mechanical properties. The former is mainly determined by the hot rolling parameters, and the latter by recrystallization, grain growth, and transformation. Thus, product quality depends on the mechanical, thermal, and microstructural behavior of the stock during plate rolling. Therefore, it is an issue to study the effects of rolling process parameters on the thermomechanics and microstructure of the stock. Presently, finite element method ( F E M ) is an effective method combining physical metallurgy with computer numerical simulation technique to simulate different metallurgical phenomena in the hot rollingcz*31.In early 1990, Pietrzyk MC4’predicted distributions of grain size in hot rolling by combining FEM with metallurgical models. Later, Karhausen Kcs1et a1 proposed their hot strip rolling simulation models, in which the microstructural evolution was
taken into consideration. However, their studies focused on a single pass, and the multi-pass continuous rolling process was not included. Thereafter, the problem was removed by Zhou SCS1 developing integrated models for hot strip continuous rolling. However, few literatures related to the plate rolling are reported, which take microstructure evolution into account. T h u s , based on microstructural evolution laws, a coupling thermomechanical and microstructural simulation model for the plate rolling was established with the aid of rigid-viscoplastic FEM in the present study. Using the model, the effects of process parameters such as reduction and deformation temperature on the deformation and microstructure of the rolled stock were studied. At the same time, distributions of different field variables were obtained after a plate rolling process with the typical technology was analyzed.
1 Mathematical Models Three main parts are involved in the FEM model. T h e first is calculation of metal flow of workpiece in the roll gap to obtain the distribution of
Foundstion Item:Item Sponsored by National Natural Science Foundation of China (50435010, 50705080) I Provincial Natural Science Foundation of Hebei Province of China (E2008000809) Revised Date: July 20, 2007 Blogrrphyr LI Xuetong(l976-), Male, Doctor, Associate Professor1 Email: xtli@ysu. edu. cnl
Issue 4
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
strain, stress, and strain rate. The second is computation of the temperature fields of plate and roll. The last part is determination of the microstructural evolution such as grain size and recrystallized fraction and cooling transformation.
1 . 1 Metal flow model The analysis of the plate rolling process makes use of the rigid-viscoplastic FEM based on the flow formulation of the penalized form of the incompressibility. According to the variational principleL7], the basic equation for the finite element formulation is expressed as: 88 2dV-I-K V
;&,dV-
Fi8uidS=0
(1)
SF
where a is the equivalent stress; is the equivalent strain rate; Fiis the surface traction; ui represents the velocity field; V is the deformation body volume; S is the integrated area; 6 is variational symbol; K is the penalty constant; and Ev is the volumetric strain rate. The stock's material is 16Mn. It is assumed that the material is isotropic and the yielding behavior follows the Von Mises yield criterion. The following equation is used to model the material behavior:
a= f ( c , c , T )
(2) where, 5 is the effective strain; and T is the temperature. The material flow behavior is determined by the flow stress data gained in thermomechanical simulation experiments. Contact between the rolled stock and the roll is solved using the shear model. 1. 2
Calculation models of heat transfer Hot plate rolling is a thermomechanical process analyzed by solving the heat conduction equation coupled to a deformation analysis. During the rolling process, the plate temperature distribution can be calculated using the governing partial differential equation shown in Eqn. ( 3 ) :
(3) where p is the density; C is the specific heat; k, is the thermal conductivity; q v is a heat generation term representing the heat released due to plastic work; t is time; and x , y is coordinate variables. The heat transfer mechanism is very complicated during hot rolling. Between passes, heat is lost by convection and radiation to the air, and more rapidly during descaling or cooling by water. After the
43
rolled stock enters the rolling deformation region, the heat generation will occurs owing to the energy of plastic deformation and friction work at the contact surface. Moreover, contact with the roll, under load, provides an efficient conduction path to a heat sink, which results in a sudden temperature drop of the stock's surface. However, on emerging from the roll stand, the surface quickly recalesces by heat flowing from the stock's center. The heat transfer mechanism during hot strip rolling is shown schematically in Fig. 1. 1. 2. 1 A i r convection a n d radiation For the interstand cooling, heat loss q1 is calculated in a standard manner: q1 = A S ( T - E )+ h , ( T - T.) (4) where T. is the ambient temperature; S is StefanBoltzmann constant; A is emissivity; and h, is air convection coefficient. T h e values of A and h, were determined by experiment. 1.2.2 W a t e r cooling Water cooling in the hot rolling process mainly contains descaling water and cooling water, which are calculated in terms of convection heat transfer. Descale sprays are usually located before the entrance of the rolling stand. An effective heat transfer coefficient can be determined by experiments. Ref. [S] concluded that for high water pressure, the value between 21 and 25 kW m-' "C-' is favorably used. Plociennik CCs3proposed the values ranging from 10 to 20 kW m-' * 'C-'. T h e water cooling system used in the plate mill is laminar jets. Kumar A"'' suggested an average value of 0.9- 1.3 kW m-' C - ' for laminar water cooling. An empirical equationc6' was provided relating determination of the value to the rolling speed. In this study,. a given heat flux density is applied to the present model. 1.2. 3 Contact heat t r a n s f e r In the hot rolling process, a thermal contact resistance exists between roll and stock, whose magnitude is related to the surface conditions, materials properties, and contact behavior, etc. There are several references available["'. However, it is difficult to accurately describe the contact heat transfer process using general mathematical equation, Moreover, several researchers think that the contact heat transfer coefficient in a certain hot rolling can be determined through experiments. T h e contact heat loss ( q 2 ) model used in this study is expressed as: qz=hc(T-Ta) (5)
-
44 ’
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Journal of Iron and Steel Research, International
+-- t--+
Air convection
- - s:
“I
--
vz
heat generation-
7
Fig. 1 Heat transfer mechanism during hot rolling
density. These changes not only affect the resistance where h, is the contact heat exchange coefficient and of metal deformation directly, but also, t o a great must be determined by experiment. extent, determine the final microstructure and prop1.2. 4 Heat generation o f f r i c t i o n erties of the rolled product. The friotisn heat q3 between stock and roll is The equations describing the microstructure evoluwritten a s r tion are usually semi-empirical. Therefore, some certain q3=kfIr Avl (6) limitations are involved with respect to the steel where r is the friction forcer A;p, iffrelative velocity compositions and process parameter ranges. These of movement 1 and R, ia the B i ~ t ~ l b ~ tcoefficient kfi of heat. As for the hot rolling, kr LR equal to @ , f i t thgl equations of the microstructural events are obtained is to say, the total friction heat is avertqpdy a l l ~ ~ a $ e t j gnder the isothermal condition. T h u s , it is clearly into the stock and into the roll. igappropriate for an industrial rolling schedule. T o settle the problem, Sellars CclZ’defined a temperature compgngated time to compute the recrystallized 1 . 3 Models of microstructural evolution Austenite grain evolution of hot deformation is fraction of austenite, and the additivity rule was inone of the physical metallurgical phenomena, whose troduced to account for the effect of non-isothermal evolution pattern mainly consists of four types, conditions on grain growth. T h e equations of the namely, dynamic recrystallization (DRX) during hot microstructure evolution used in this study can be deformation, static recrystallization ( SRX 1 and seen in Ref. [13]. After rolling at last pass, the rolled stock will metadynamic recrystallization (MRX) after deformenter the cooling tables to cool. A s the temperature ation as well as grain growth after complete recrysof the stock decreases, the transformation from austallization when the dynamic and static recoveries are tenite to lower temperature phases will occur. T h e ignored. DRX involves the nucleation and growth of model currently only considers the transformation new grains when the dislocation denrslty during defrom austenite to ferrite and pearlite in predominantformation exceeds a critical value, MRX is the conly ferrite microstructures. However, the main patinuation of the growth of dynamically recrystallized rameter of interest in plain carbon steels is the fernuclei after deformation has been interrupted. SRX rite grain size because the pearlite content and interinvolves the nucleation and growth of new strainlamellar spacing do not contribute significantly to free grains preferentially in zones of high dislocation
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
the strength at these compositions ( C,, < 0.45, where C , , = w c + w M , / 6 ) .T h e factors that affect the ferrite grain size are the austenite grain size and the retained strain before transformation, which relate to the deformation history, composition, and cooling rate, which are, largely, external influences. Th e ferrite grain size, d:, for transformation from completely recrystallized austenite is expressed as : d : = a f b ?-o.5+c[1-eexp(-l.
5 X 10-'d,)]
(7)
where T is the cooling rate; d, is the austenite grain size; and a , b , c are constants, which are 1 . 4 , 5 . 0 , and 22.0, respectively, for C-Mn steel. Any retained strain present in the austenite during transformation will refine the ferrite grain size. The model by Sellars is also used for thisc"' : d, =d: ( 1-0. 45& ) (8) where E , is the retained strain. Based on the microstructural evolution law described above, a calculation flow chart for hot rolling is developed and shown in Fig. 2. In the present model, the DRX will be calculated when the equivalent strain rate is greater than zero. On the contrary, the softening processes of MRX and SRX will be solved. When the recrystallization is not complete, a mean grain size Z can be computed according to the following equation: d = Xd,,, -k (1- X)do (9) where do is the grain size before each pass; and d,. is the recrystallized grain size. This mean grain size is regarded as the size of the initial grain for the next pass rolling. It is possible to have partial MRX or SRX recry-
1
t
I
Ec--criticd
]
FE analysis .
2
FE Model of Plate Rolling
Based on a certain 4-high reversing plate mill, a coupling microstructural evolution FE model has been established using nonlinear rigid-viscoplastic FEM. Generally, nine passes are involved in the rolling process, whose technological process is shown in Fig. 3. After it bears a longitudinal rolling deformation, the stock is tilted by 90" to be rolled transversely by two passes. Here, the expected rolled stock width is obtained. After that, the stock is tilted by 90" again and continues to be rolled transversely to the final product. It is very difficult to build a simulation model for the whole process of plate rolling owing to multiple pass and large deformation. Therefore, a single pass FE model was built t o reduce the solution time. However, the data transmission from a rolling pass to the next pass is completed by compiling an interpolation routine. The FE model built is shown in Fig. 4,
s ~ *
r, -Transformation X-Recrystallization Kx-COnstant
F , e, 1
stallization aiter one pass with strain E ~ which , will introduce a mixed microstructure prior to the next deformation of strain e2. When modeling the recrystallized behavior of the second pass, an initial effective strain of k, (1 - X ) Q c151 is added t o e2 , where k, is a constant, for C-Mn steels, k, = 1.
€-Strain
Initialization
temperature
fraction
Fig. 3
Technological process of plate rolling
. &.. T
t
Fig. 2
Flow chart of analyzing microstructure
45
Fig. 4
FE model
Journal of Iron and Steel Research, International
46
in which the stock is meshed using hexahedral element with eight nodes and the total number is 10 000. Fig. 5 shows a quarter mesh of workpiece transverse section and four typical positions analyzed.
Vol. 15
grain distributions are presented after a plate rolling process with a typical process is simulated using model described above.
Influence of reduction Reduction in pass directly influences plastic strain, thereby influencing heat generation from plastic work. T o make the initial temperature field close to the practical rolling conditions, stocks analyzed are cooled for 30 s before rolling. Fig. 6 presents the temperature curves at four typical positions of the stock.
3.1
3 Results and Discussion The typical steel 16Mn is used to investigate the effects of process parameters such as reduction, temperature, and rolling speed on thermomechanical and microstructural behaviors, whose basic calculation conditions are shown in Table 1, and then, the calculated austenite grain and transformed ferrite Width direction
Width symmetry plane
\ 4
1
3
2 hic chess symmetiy plane
Fig. 5
z
d
x
Position of pohb laplyzed
Table 1 cplcpI.tion porpmetcrs Thicknesdmm
Initial grain size/pm Temperature/ C Velocity/( m s-'
0
1 100 1 000
200
200 60
130
1.2
0.6
1.8
TimdS
Fig. 6 Temperntore field than-
during the rolling
From Fig. 6, it can be seen that the simulated temperature distribution trend is basically in agreement with the theoretical analysis. Owing to the relatively cold roll, the stock surface temperature drops rapidly in the roll gaps and rises slowly thereafter. The center temperature of the stock increases somewhat in the roll gaps owing to the deformation heat
2
)
Roll diametedmm Roll temperature/ Y: 980
80
and decreases slowly in the interpasses owing to the heat loss by convection and radiation. Fig. 7 presents the surface temperature distribution at the exit of rolling vs. relative reduction. Since the surface temperature is affected by both contact heat loss and heat conduction from high temperature zone owing to plastic heat, based on the simulated results, the surface temperature of stock with thickness of 200 mm first decreases with increasing reduction, and then rises slowly. However, the surface temperature of the stock with thickness of 60 mm always increases with increasing reduction. DRX occurrence needs enough plastic deformation and deformation temperature. Fig. 8 provides the effect of relative reduction on DRX fraction when the thickness of the stock is 200 mm. It can be known that DRX occurs only as the relative reduction exceeds 30%, and subsequently, the recrystallized fraction increases rapidly with increasing reduction. On rolling stock of 60 mm in thickness using lower deformation temperature, DRX almost does not occur,
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
47
2 10 0
Thickness=20 mm
20 30 Relative reduction86
10
Fig. 7
40
I 0
Surface temperature of the stock after rolling
0.5
1.0 1.5 Timds
2.0
2.5
Fig. 10 Mean grain size change during the rolling
0.20
25
Fig. 8
fined by DRX and SRX, whose evolution trend is basically in agreement with the SRX fraction. T h e effect of reduction on the mean grain size after rolling is shown in Fig. 11. From the figure, it is seen that the mean grain size is more and more refined with increasing reduction. Meanwhile, the grain sizes at the surface and center of the stock also approach accordance increasingly. Hence, it is very effective for increasing the reduction to refine grain.
Thickness=200mm
.
30 35 Relative reduction86
40
Variation of DRX fraction with reduction
Fig. 9 shows the SRX fraction changing at four representative points of the stock after a certain rolling. SRX fraction increases with delaying time, and the recrystallized fractions of 2 , 1 , 3 reach a steady value in order. The mean grain size changing during rolling is demonstrated in Fig. 10. Austenite grain is
Influence of deformation temperature Temperature is one of the key factors influencing microstructural evolution during hot deformation. Fig. 12 presents the influencing laws of deformation temperature on the temperature rise at the stock center (point 2), in which it can be clearly seen that temperature rise at the center decreases linearly with initial rolling temperature increase. The simulated influences of deformation temper-
3.2
1.0
Thickness=200mm
0.8 0.6 0
0.4
Thickness=60mm Relative reduction=26% 4
0
Fig. 9
8 Tim&
12
16
SRX fraction after rolling
20
10
20 30 Relative reductiofi
40
Fig. 11 Effect of reduction on mean grain size after rolling
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Journal of Iron and Steel Research, International
48
T h e mean grain size after rolling is calculated by averaging the recrystallized grain size and the initial grain size according to their volume fraction. T h u s , the mean grain size may not change monotonously with increasing deformation temperature. T h e predicted result is illustrated in Fig. 15. It can be seen that the mean grain size is first reduced, and then increased with deformation temperature rising. Therefore, proper deformation temperature used in rolling can refine the austenite grain.
~~~
960
1060
1000
1100
1 160
5200
Deformation temperaturdc
3.3
Fig. 12 Effect of deformation temperature on temperature rise at stock center
ature on the SXR fraction and grain size are shown in Fig. 13 and Fig. 1 4 , respectively. T h e SRX grain size becomes more refined with reducing rolling temperature, and the SRX speed is quickened when the deformation temperature rises.
Influence of rolling speed
The predicted temperature rise at the center using different rolling speeds is shown in Fig. 16. From the figure, it is seen that the temperature rise is increasing with increasing rolling speed. T h e influence of rolling speed on mean grain size after rolling is demonstrated in Fig. 17. For the stock with the thickness of 200 mm, the mean grain size does not almost
r=2W
180
.1 e2
1.0
0.8
5 140
1
i
loo
0.2
B
0 30.0
31.0
32.0
33.0
Tim&
60 1000 1060 1100 1160 Deformation temperaturd
960
Fig. 13 Effect of temperature on SRX kinetics
Fig. 15 Effect of deformation temperature on mean grain size after rolling
/I
100 Thickness=60mm
1200
80
40 ~~
I 960
1000
1060
1100
1160
1200
Deformation temperature/t
Fig. 14 Effect of temperature on SRX grain size
1.0
2.0 3.0 Rolling speed/(md)
4.0
Fig. 16 Effect of rolling speed on temperature rise at center of stock
49
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
1
loo
1u
Equivalent strain rate
Thickness=60 mm
ti
4 Q
4
3
0 1 1.0
Simulation on a typical plate rolling process In this simulation, the initial thickness, width, and temperature of the stock are 250 mm, 1 900 mm and 1 100 " C , respectively. The initial austenite grain size is assumed to be 200 pm. The roll diameter is 980 mm, and the other process parameters are shown in Table 2. The FE analysis of a plate rolling of steel 16Mn was carried out using the F E model described above. The predicted distributions of average equivalent strain and strain rate in the thickness direction are shown in Fig. 18. From the figure, it is seen that a larger plastic deformation occurs at the second pass to gain a great spread in the cross direction. In the later passes, the plastic strain change is not large. In the last pass, a large plastic deformation is obtained for refining grain and for improving product proper3.4
4
5
6
7
8
ties. The mean equivalent strain rate distribution basically increases with rolling pass number increasing. However, these are less than 10 s - l , whose maximal value is about 8 s-'. T h e simulated austenite grain size distributions in the width symmetrical plane are presented in Fig. 19. It can be seen that the grain size is refined greatly during the first two rolling passes. Subsequently, the grain size does not change largely by the actions of deformation refinement and interval grain growth at the later passes. The mean grain size predicted before transformation is about 43 pm. Fig. 20 shows the temperature and transformed ferrite grain size distributions during laminar cooling. Transformed ferrite grain at the surface of the stock occurs earlier than that of the rolled stock center owing to different cooling speed. T h e difference in their sizes is not great. T h e ferrite grain grade was measured as about 9 at the plate center and 9.5 near the surface, whose metallograph is shown in Fig. 21. Therefore, the predicted ferrite grain size 200
y
-1 ....2
160 .
Table 2 Rolling schedule Pass
Rolling mode
Reduction/mm
Velocity/(m * s-l)
1
10
2
L (Longitudinal) T (Transverse)
40
3
T
30
4
30
5
L L
6
L
25
1. 2 1. 5 1. 5 1. 7 2.0 2. 0
7
L L
20
2. 2
8
15
2. 5
9
L
15
2. 5
9
Fig. 18 Average equivalent strain and strain rate for different passes
Fig. 17 Effect of rolling speed on mean grain size at center of plate
change. When the thickness is 60 mm, the mean grain size reduces with increasing rolling speed. T h u s , increasing the rolling speed at the final rolling passes can refine grain effectively.
3
Pass
4.0
2.0 3.0 Rolling speed/(md)
25
2
Fi 120 .
3 f!
. . . ... . . ..
0
40
.
Fig. 19 History of austenite mean grain size variation
Journal of Iron a n d Steel Research, International
50
20
Oo0 Temperature
300
320
agrees - well with the measurement.
4
. 310
350
330 340 Timds
360
Fig. 20 Ferrite transformation during cooling
(a) Surface!
Fig. 21
Conclusions
(1) Based on austenite microstructural evolution law during hot deformation, an integrated F E model for coupling multivariable plate rolling was developed using the rigid viscoplastic FEM. Using the model, the influences of process parameters on the deformation parameters and microstructure of the stock were investigated. (2) Aiming at a certain plate mill, an FE analysis with the typical process parameters was carried out using the FE model. Based on the simulation r e
(b) Center
Ferrite gain size metallograph of plate
sults, the distributions of various field-variables such as strain, strain rate, and microstructure are presented, and the predicted ferrite grain size is in good agreement with the measured one. Thus, it is seen that the FE model built in this study possesses favorable practicability and accuracy and can be used to study process parameters and to optimize draft schedules. References: CHEN Jian-jiu, HE Da-lun. Controlled Rolling and Controlled Cooling Technologies Used in Modern Wide Heavy Plate Mill [J]. Baosteel Technol, 1999, l O ( 2 ) : 10 (in Chinese). Wells M A, Lloyd D J , Samarasekera I V , et a]. Modeling the Microstructural Changes During Hot Tandem Rolling of AASXXX Aluminum Alloys: Part I Microstructural Evolution [J]. Metall Mater Trans, 1998, 29B(3): 611. WANG Min-ting, LI Xuetong. DU Feng-shan, et al. A Coupled Thermal-Mechanical and Microstructural Simulation of the Cross Wedge Rolling Process and Experimental Verification [J]. Mater Sci Eng, 2005, 391A: 305. Pietrzyk M. FE Based Model of Structure Development in the Hot Rolling Process [J]. Steel Res, 1990, 61(12): 603. Karhausen K , Kopp T. Model for Integrated Process and Microstructure Simulation in Hot Forming [J]. Steel Res, 1992, 63(6) : 247. Zhou S X. An Integrated Model for Hot Rolling of Steel Strips
.
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[J]. J Mater Process Technol, 2003, (134) : 338. Kobayashi S, Oh S, Altan T. Metal Forming and the FiniteElement Method [MI. New York: Oxford University Press, 1989. Devadas C, Samarasekera I V. Heat Transfer During Hot Rolling of Steel Strip [J]. Ironmak Steelmak, 1986, l ( 6 ) : 311. Plocinniek C, Sauer W , Meyer P. A Numerical Model for Heat Transfer Analysis of Strip Rolled in Steckel Mills [A]. Beynon J , Ingham P , Teichert H , et al, eds. Proceedings of the 2nd International Conference Modeling of Metal Rolling Processes [C]. London: Institute of Materials, 1996. 531. Kumar A , McCulloch C , Hawbolt E B, et al. Modeling Thermal and Microstructural Evolution on Runout Table of Hot Strip Rolling [J]. Mater Sci Technol, 1991, 7(4): 360. Goldsmith A, Waterma T. Handbook of Thermophysical Properties of Solid Materials [MI. New York: Maanillan, 1961. Sellars C M, Whiteman A. Recrystallization and Grain Growth in Hot Rolling [J]. Met Science, 1979, 13: 187. Maccagno T M, Jonas J J , Hodgson P D. Spreadsheet Modeling of Grain Size Evolution During Rod Rolling [J]. ISIJ Int, 1996, 36(6): 720. Fulvio Siciliano J r , Jonas J J. Mathematical Modeling of the Hot Strip Rolling of Microalloyed Nb, Multiply-Alloyed CrMo, and Plain C-Mn Steels [J]. Metall Mater Trans, 2000, 31A(2): 511. Hodgson P D, Gibbs R K. A Mathematical Model to Predict the Mechanical Properties of Hot Rolled C-Mn and Microalloyed Steels [J]. ISIJ Int, 1992, 32(12): 1329.
Y0ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNPLIIONAL. 2008, 15(4) : 42-50
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process LI Xue-tong ,
WANG Min-ting ,
DU Feng-shan
(College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China)
Abstract: Using three-dimensional rigid-viscoplastic finite element method (FEM) , a coupling multivariable numerical simulation model for steel plate rolling has been established based on the physical metallurgy microstructural evolution rule and experiential equations. The effects of reduction, deformation temperature, and rolling speed on the deformation parameters and microstructure in plate rolling were investigated using the model. After a typical rolling process of steel plate 16Mn is simulated, the strain, temperature, and microstructure distributions are presented, as well as the ferrite grain transformation during the period of cooling. By comparing the calculated ferrite grain sizes with measured ones, the model is validated. Key words: hot rolling; plate; FEMi microstructure; coupling
A large variety of plates, as important iron and steel materials, are widely applied to shipbuilding, petrochemical industry, machine manufacturing, and so onC1’. In hot plate rolling, one side is to perform thickness reduction, and the other is to achieve grain refinement of austenite, which generally causes good complex mechanical properties. The former is mainly determined by the hot rolling parameters, and the latter by recrystallization, grain growth, and transformation. Thus, product quality depends on the mechanical, thermal, and microstructural behavior of the stock during plate rolling. Therefore, it is an issue to study the effects of rolling process parameters on the thermomechanics and microstructure of the stock. Presently, finite element method ( F E M ) is an effective method combining physical metallurgy with computer numerical simulation technique to simulate different metallurgical phenomena in the hot rollingcz*31.In early 1990, Pietrzyk MC4’predicted distributions of grain size in hot rolling by combining FEM with metallurgical models. Later, Karhausen Kcs1et a1 proposed their hot strip rolling simulation models, in which the microstructural evolution was
taken into consideration. However, their studies focused on a single pass, and the multi-pass continuous rolling process was not included. Thereafter, the problem was removed by Zhou SCS1 developing integrated models for hot strip continuous rolling. However, few literatures related to the plate rolling are reported, which take microstructure evolution into account. T h u s , based on microstructural evolution laws, a coupling thermomechanical and microstructural simulation model for the plate rolling was established with the aid of rigid-viscoplastic FEM in the present study. Using the model, the effects of process parameters such as reduction and deformation temperature on the deformation and microstructure of the rolled stock were studied. At the same time, distributions of different field variables were obtained after a plate rolling process with the typical technology was analyzed.
1 Mathematical Models Three main parts are involved in the FEM model. T h e first is calculation of metal flow of workpiece in the roll gap to obtain the distribution of
Foundstion Item:Item Sponsored by National Natural Science Foundation of China (50435010, 50705080) I Provincial Natural Science Foundation of Hebei Province of China (E2008000809) Revised Date: July 20, 2007 Blogrrphyr LI Xuetong(l976-), Male, Doctor, Associate Professor1 Email: xtli@ysu. edu. cnl
Issue 4
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
strain, stress, and strain rate. The second is computation of the temperature fields of plate and roll. The last part is determination of the microstructural evolution such as grain size and recrystallized fraction and cooling transformation.
1 . 1 Metal flow model The analysis of the plate rolling process makes use of the rigid-viscoplastic FEM based on the flow formulation of the penalized form of the incompressibility. According to the variational principleL7], the basic equation for the finite element formulation is expressed as: 88 2dV-I-K V
;&,dV-
Fi8uidS=0
(1)
SF
where a is the equivalent stress; is the equivalent strain rate; Fiis the surface traction; ui represents the velocity field; V is the deformation body volume; S is the integrated area; 6 is variational symbol; K is the penalty constant; and Ev is the volumetric strain rate. The stock's material is 16Mn. It is assumed that the material is isotropic and the yielding behavior follows the Von Mises yield criterion. The following equation is used to model the material behavior:
a= f ( c , c , T )
(2) where, 5 is the effective strain; and T is the temperature. The material flow behavior is determined by the flow stress data gained in thermomechanical simulation experiments. Contact between the rolled stock and the roll is solved using the shear model. 1. 2
Calculation models of heat transfer Hot plate rolling is a thermomechanical process analyzed by solving the heat conduction equation coupled to a deformation analysis. During the rolling process, the plate temperature distribution can be calculated using the governing partial differential equation shown in Eqn. ( 3 ) :
(3) where p is the density; C is the specific heat; k, is the thermal conductivity; q v is a heat generation term representing the heat released due to plastic work; t is time; and x , y is coordinate variables. The heat transfer mechanism is very complicated during hot rolling. Between passes, heat is lost by convection and radiation to the air, and more rapidly during descaling or cooling by water. After the
43
rolled stock enters the rolling deformation region, the heat generation will occurs owing to the energy of plastic deformation and friction work at the contact surface. Moreover, contact with the roll, under load, provides an efficient conduction path to a heat sink, which results in a sudden temperature drop of the stock's surface. However, on emerging from the roll stand, the surface quickly recalesces by heat flowing from the stock's center. The heat transfer mechanism during hot strip rolling is shown schematically in Fig. 1. 1. 2. 1 A i r convection a n d radiation For the interstand cooling, heat loss q1 is calculated in a standard manner: q1 = A S ( T - E )+ h , ( T - T.) (4) where T. is the ambient temperature; S is StefanBoltzmann constant; A is emissivity; and h, is air convection coefficient. T h e values of A and h, were determined by experiment. 1.2.2 W a t e r cooling Water cooling in the hot rolling process mainly contains descaling water and cooling water, which are calculated in terms of convection heat transfer. Descale sprays are usually located before the entrance of the rolling stand. An effective heat transfer coefficient can be determined by experiments. Ref. [S] concluded that for high water pressure, the value between 21 and 25 kW m-' "C-' is favorably used. Plociennik CCs3proposed the values ranging from 10 to 20 kW m-' * 'C-'. T h e water cooling system used in the plate mill is laminar jets. Kumar A"'' suggested an average value of 0.9- 1.3 kW m-' C - ' for laminar water cooling. An empirical equationc6' was provided relating determination of the value to the rolling speed. In this study,. a given heat flux density is applied to the present model. 1.2. 3 Contact heat t r a n s f e r In the hot rolling process, a thermal contact resistance exists between roll and stock, whose magnitude is related to the surface conditions, materials properties, and contact behavior, etc. There are several references available["'. However, it is difficult to accurately describe the contact heat transfer process using general mathematical equation, Moreover, several researchers think that the contact heat transfer coefficient in a certain hot rolling can be determined through experiments. T h e contact heat loss ( q 2 ) model used in this study is expressed as: qz=hc(T-Ta) (5)
-
44 ’
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Journal of Iron and Steel Research, International
+-- t--+
Air convection
- - s:
“I
--
vz
heat generation-
7
Fig. 1 Heat transfer mechanism during hot rolling
density. These changes not only affect the resistance where h, is the contact heat exchange coefficient and of metal deformation directly, but also, t o a great must be determined by experiment. extent, determine the final microstructure and prop1.2. 4 Heat generation o f f r i c t i o n erties of the rolled product. The friotisn heat q3 between stock and roll is The equations describing the microstructure evoluwritten a s r tion are usually semi-empirical. Therefore, some certain q3=kfIr Avl (6) limitations are involved with respect to the steel where r is the friction forcer A;p, iffrelative velocity compositions and process parameter ranges. These of movement 1 and R, ia the B i ~ t ~ l b ~ tcoefficient kfi of heat. As for the hot rolling, kr LR equal to @ , f i t thgl equations of the microstructural events are obtained is to say, the total friction heat is avertqpdy a l l ~ ~ a $ e t j gnder the isothermal condition. T h u s , it is clearly into the stock and into the roll. igappropriate for an industrial rolling schedule. T o settle the problem, Sellars CclZ’defined a temperature compgngated time to compute the recrystallized 1 . 3 Models of microstructural evolution Austenite grain evolution of hot deformation is fraction of austenite, and the additivity rule was inone of the physical metallurgical phenomena, whose troduced to account for the effect of non-isothermal evolution pattern mainly consists of four types, conditions on grain growth. T h e equations of the namely, dynamic recrystallization (DRX) during hot microstructure evolution used in this study can be deformation, static recrystallization ( SRX 1 and seen in Ref. [13]. After rolling at last pass, the rolled stock will metadynamic recrystallization (MRX) after deformenter the cooling tables to cool. A s the temperature ation as well as grain growth after complete recrysof the stock decreases, the transformation from austallization when the dynamic and static recoveries are tenite to lower temperature phases will occur. T h e ignored. DRX involves the nucleation and growth of model currently only considers the transformation new grains when the dislocation denrslty during defrom austenite to ferrite and pearlite in predominantformation exceeds a critical value, MRX is the conly ferrite microstructures. However, the main patinuation of the growth of dynamically recrystallized rameter of interest in plain carbon steels is the fernuclei after deformation has been interrupted. SRX rite grain size because the pearlite content and interinvolves the nucleation and growth of new strainlamellar spacing do not contribute significantly to free grains preferentially in zones of high dislocation
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
the strength at these compositions ( C,, < 0.45, where C , , = w c + w M , / 6 ) .T h e factors that affect the ferrite grain size are the austenite grain size and the retained strain before transformation, which relate to the deformation history, composition, and cooling rate, which are, largely, external influences. Th e ferrite grain size, d:, for transformation from completely recrystallized austenite is expressed as : d : = a f b ?-o.5+c[1-eexp(-l.
5 X 10-'d,)]
(7)
where T is the cooling rate; d, is the austenite grain size; and a , b , c are constants, which are 1 . 4 , 5 . 0 , and 22.0, respectively, for C-Mn steel. Any retained strain present in the austenite during transformation will refine the ferrite grain size. The model by Sellars is also used for thisc"' : d, =d: ( 1-0. 45& ) (8) where E , is the retained strain. Based on the microstructural evolution law described above, a calculation flow chart for hot rolling is developed and shown in Fig. 2. In the present model, the DRX will be calculated when the equivalent strain rate is greater than zero. On the contrary, the softening processes of MRX and SRX will be solved. When the recrystallization is not complete, a mean grain size Z can be computed according to the following equation: d = Xd,,, -k (1- X)do (9) where do is the grain size before each pass; and d,. is the recrystallized grain size. This mean grain size is regarded as the size of the initial grain for the next pass rolling. It is possible to have partial MRX or SRX recry-
1
t
I
Ec--criticd
]
FE analysis .
2
FE Model of Plate Rolling
Based on a certain 4-high reversing plate mill, a coupling microstructural evolution FE model has been established using nonlinear rigid-viscoplastic FEM. Generally, nine passes are involved in the rolling process, whose technological process is shown in Fig. 3. After it bears a longitudinal rolling deformation, the stock is tilted by 90" to be rolled transversely by two passes. Here, the expected rolled stock width is obtained. After that, the stock is tilted by 90" again and continues to be rolled transversely to the final product. It is very difficult to build a simulation model for the whole process of plate rolling owing to multiple pass and large deformation. Therefore, a single pass FE model was built t o reduce the solution time. However, the data transmission from a rolling pass to the next pass is completed by compiling an interpolation routine. The FE model built is shown in Fig. 4,
s ~ *
r, -Transformation X-Recrystallization Kx-COnstant
F , e, 1
stallization aiter one pass with strain E ~ which , will introduce a mixed microstructure prior to the next deformation of strain e2. When modeling the recrystallized behavior of the second pass, an initial effective strain of k, (1 - X ) Q c151 is added t o e2 , where k, is a constant, for C-Mn steels, k, = 1.
€-Strain
Initialization
temperature
fraction
Fig. 3
Technological process of plate rolling
. &.. T
t
Fig. 2
Flow chart of analyzing microstructure
45
Fig. 4
FE model
Journal of Iron and Steel Research, International
46
in which the stock is meshed using hexahedral element with eight nodes and the total number is 10 000. Fig. 5 shows a quarter mesh of workpiece transverse section and four typical positions analyzed.
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grain distributions are presented after a plate rolling process with a typical process is simulated using model described above.
Influence of reduction Reduction in pass directly influences plastic strain, thereby influencing heat generation from plastic work. T o make the initial temperature field close to the practical rolling conditions, stocks analyzed are cooled for 30 s before rolling. Fig. 6 presents the temperature curves at four typical positions of the stock.
3.1
3 Results and Discussion The typical steel 16Mn is used to investigate the effects of process parameters such as reduction, temperature, and rolling speed on thermomechanical and microstructural behaviors, whose basic calculation conditions are shown in Table 1, and then, the calculated austenite grain and transformed ferrite Width direction
Width symmetry plane
\ 4
1
3
2 hic chess symmetiy plane
Fig. 5
z
d
x
Position of pohb laplyzed
Table 1 cplcpI.tion porpmetcrs Thicknesdmm
Initial grain size/pm Temperature/ C Velocity/( m s-'
0
1 100 1 000
200
200 60
130
1.2
0.6
1.8
TimdS
Fig. 6 Temperntore field than-
during the rolling
From Fig. 6, it can be seen that the simulated temperature distribution trend is basically in agreement with the theoretical analysis. Owing to the relatively cold roll, the stock surface temperature drops rapidly in the roll gaps and rises slowly thereafter. The center temperature of the stock increases somewhat in the roll gaps owing to the deformation heat
2
)
Roll diametedmm Roll temperature/ Y: 980
80
and decreases slowly in the interpasses owing to the heat loss by convection and radiation. Fig. 7 presents the surface temperature distribution at the exit of rolling vs. relative reduction. Since the surface temperature is affected by both contact heat loss and heat conduction from high temperature zone owing to plastic heat, based on the simulated results, the surface temperature of stock with thickness of 200 mm first decreases with increasing reduction, and then rises slowly. However, the surface temperature of the stock with thickness of 60 mm always increases with increasing reduction. DRX occurrence needs enough plastic deformation and deformation temperature. Fig. 8 provides the effect of relative reduction on DRX fraction when the thickness of the stock is 200 mm. It can be known that DRX occurs only as the relative reduction exceeds 30%, and subsequently, the recrystallized fraction increases rapidly with increasing reduction. On rolling stock of 60 mm in thickness using lower deformation temperature, DRX almost does not occur,
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
47
2 10 0
Thickness=20 mm
20 30 Relative reduction86
10
Fig. 7
40
I 0
Surface temperature of the stock after rolling
0.5
1.0 1.5 Timds
2.0
2.5
Fig. 10 Mean grain size change during the rolling
0.20
25
Fig. 8
fined by DRX and SRX, whose evolution trend is basically in agreement with the SRX fraction. T h e effect of reduction on the mean grain size after rolling is shown in Fig. 11. From the figure, it is seen that the mean grain size is more and more refined with increasing reduction. Meanwhile, the grain sizes at the surface and center of the stock also approach accordance increasingly. Hence, it is very effective for increasing the reduction to refine grain.
Thickness=200mm
.
30 35 Relative reduction86
40
Variation of DRX fraction with reduction
Fig. 9 shows the SRX fraction changing at four representative points of the stock after a certain rolling. SRX fraction increases with delaying time, and the recrystallized fractions of 2 , 1 , 3 reach a steady value in order. The mean grain size changing during rolling is demonstrated in Fig. 10. Austenite grain is
Influence of deformation temperature Temperature is one of the key factors influencing microstructural evolution during hot deformation. Fig. 12 presents the influencing laws of deformation temperature on the temperature rise at the stock center (point 2), in which it can be clearly seen that temperature rise at the center decreases linearly with initial rolling temperature increase. The simulated influences of deformation temper-
3.2
1.0
Thickness=200mm
0.8 0.6 0
0.4
Thickness=60mm Relative reduction=26% 4
0
Fig. 9
8 Tim&
12
16
SRX fraction after rolling
20
10
20 30 Relative reductiofi
40
Fig. 11 Effect of reduction on mean grain size after rolling
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Journal of Iron and Steel Research, International
48
T h e mean grain size after rolling is calculated by averaging the recrystallized grain size and the initial grain size according to their volume fraction. T h u s , the mean grain size may not change monotonously with increasing deformation temperature. T h e predicted result is illustrated in Fig. 15. It can be seen that the mean grain size is first reduced, and then increased with deformation temperature rising. Therefore, proper deformation temperature used in rolling can refine the austenite grain.
~~~
960
1060
1000
1100
1 160
5200
Deformation temperaturdc
3.3
Fig. 12 Effect of deformation temperature on temperature rise at stock center
ature on the SXR fraction and grain size are shown in Fig. 13 and Fig. 1 4 , respectively. T h e SRX grain size becomes more refined with reducing rolling temperature, and the SRX speed is quickened when the deformation temperature rises.
Influence of rolling speed
The predicted temperature rise at the center using different rolling speeds is shown in Fig. 16. From the figure, it is seen that the temperature rise is increasing with increasing rolling speed. T h e influence of rolling speed on mean grain size after rolling is demonstrated in Fig. 17. For the stock with the thickness of 200 mm, the mean grain size does not almost
r=2W
180
.1 e2
1.0
0.8
5 140
1
i
loo
0.2
B
0 30.0
31.0
32.0
33.0
Tim&
60 1000 1060 1100 1160 Deformation temperaturd
960
Fig. 13 Effect of temperature on SRX kinetics
Fig. 15 Effect of deformation temperature on mean grain size after rolling
/I
100 Thickness=60mm
1200
80
40 ~~
I 960
1000
1060
1100
1160
1200
Deformation temperature/t
Fig. 14 Effect of temperature on SRX grain size
1.0
2.0 3.0 Rolling speed/(md)
4.0
Fig. 16 Effect of rolling speed on temperature rise at center of stock
49
Coupling Thermomechanical and Microstructural FE Analysis in Plate Rolling Process
Issue 4
1
loo
1u
Equivalent strain rate
Thickness=60 mm
ti
4 Q
4
3
0 1 1.0
Simulation on a typical plate rolling process In this simulation, the initial thickness, width, and temperature of the stock are 250 mm, 1 900 mm and 1 100 " C , respectively. The initial austenite grain size is assumed to be 200 pm. The roll diameter is 980 mm, and the other process parameters are shown in Table 2. The FE analysis of a plate rolling of steel 16Mn was carried out using the F E model described above. The predicted distributions of average equivalent strain and strain rate in the thickness direction are shown in Fig. 18. From the figure, it is seen that a larger plastic deformation occurs at the second pass to gain a great spread in the cross direction. In the later passes, the plastic strain change is not large. In the last pass, a large plastic deformation is obtained for refining grain and for improving product proper3.4
4
5
6
7
8
ties. The mean equivalent strain rate distribution basically increases with rolling pass number increasing. However, these are less than 10 s - l , whose maximal value is about 8 s-'. T h e simulated austenite grain size distributions in the width symmetrical plane are presented in Fig. 19. It can be seen that the grain size is refined greatly during the first two rolling passes. Subsequently, the grain size does not change largely by the actions of deformation refinement and interval grain growth at the later passes. The mean grain size predicted before transformation is about 43 pm. Fig. 20 shows the temperature and transformed ferrite grain size distributions during laminar cooling. Transformed ferrite grain at the surface of the stock occurs earlier than that of the rolled stock center owing to different cooling speed. T h e difference in their sizes is not great. T h e ferrite grain grade was measured as about 9 at the plate center and 9.5 near the surface, whose metallograph is shown in Fig. 21. Therefore, the predicted ferrite grain size 200
y
-1 ....2
160 .
Table 2 Rolling schedule Pass
Rolling mode
Reduction/mm
Velocity/(m * s-l)
1
10
2
L (Longitudinal) T (Transverse)
40
3
T
30
4
30
5
L L
6
L
25
1. 2 1. 5 1. 5 1. 7 2.0 2. 0
7
L L
20
2. 2
8
15
2. 5
9
L
15
2. 5
9
Fig. 18 Average equivalent strain and strain rate for different passes
Fig. 17 Effect of rolling speed on mean grain size at center of plate
change. When the thickness is 60 mm, the mean grain size reduces with increasing rolling speed. T h u s , increasing the rolling speed at the final rolling passes can refine grain effectively.
3
Pass
4.0
2.0 3.0 Rolling speed/(md)
25
2
Fi 120 .
3 f!
. . . ... . . ..
0
40
.
Fig. 19 History of austenite mean grain size variation
Journal of Iron a n d Steel Research, International
50
20
Oo0 Temperature
300
320
agrees - well with the measurement.
4
. 310
350
330 340 Timds
360
Fig. 20 Ferrite transformation during cooling
(a) Surface!
Fig. 21
Conclusions
(1) Based on austenite microstructural evolution law during hot deformation, an integrated F E model for coupling multivariable plate rolling was developed using the rigid viscoplastic FEM. Using the model, the influences of process parameters on the deformation parameters and microstructure of the stock were investigated. (2) Aiming at a certain plate mill, an FE analysis with the typical process parameters was carried out using the FE model. Based on the simulation r e
(b) Center
Ferrite gain size metallograph of plate
sults, the distributions of various field-variables such as strain, strain rate, and microstructure are presented, and the predicted ferrite grain size is in good agreement with the measured one. Thus, it is seen that the FE model built in this study possesses favorable practicability and accuracy and can be used to study process parameters and to optimize draft schedules. References: CHEN Jian-jiu, HE Da-lun. Controlled Rolling and Controlled Cooling Technologies Used in Modern Wide Heavy Plate Mill [J]. Baosteel Technol, 1999, l O ( 2 ) : 10 (in Chinese). Wells M A, Lloyd D J , Samarasekera I V , et a]. Modeling the Microstructural Changes During Hot Tandem Rolling of AASXXX Aluminum Alloys: Part I Microstructural Evolution [J]. Metall Mater Trans, 1998, 29B(3): 611. WANG Min-ting, LI Xuetong. DU Feng-shan, et al. A Coupled Thermal-Mechanical and Microstructural Simulation of the Cross Wedge Rolling Process and Experimental Verification [J]. Mater Sci Eng, 2005, 391A: 305. Pietrzyk M. FE Based Model of Structure Development in the Hot Rolling Process [J]. Steel Res, 1990, 61(12): 603. Karhausen K , Kopp T. Model for Integrated Process and Microstructure Simulation in Hot Forming [J]. Steel Res, 1992, 63(6) : 247. Zhou S X. An Integrated Model for Hot Rolling of Steel Strips
.
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[J]. J Mater Process Technol, 2003, (134) : 338. Kobayashi S, Oh S, Altan T. Metal Forming and the FiniteElement Method [MI. New York: Oxford University Press, 1989. Devadas C, Samarasekera I V. Heat Transfer During Hot Rolling of Steel Strip [J]. Ironmak Steelmak, 1986, l ( 6 ) : 311. Plocinniek C, Sauer W , Meyer P. A Numerical Model for Heat Transfer Analysis of Strip Rolled in Steckel Mills [A]. Beynon J , Ingham P , Teichert H , et al, eds. Proceedings of the 2nd International Conference Modeling of Metal Rolling Processes [C]. London: Institute of Materials, 1996. 531. Kumar A , McCulloch C , Hawbolt E B, et al. Modeling Thermal and Microstructural Evolution on Runout Table of Hot Strip Rolling [J]. Mater Sci Technol, 1991, 7(4): 360. Goldsmith A, Waterma T. Handbook of Thermophysical Properties of Solid Materials [MI. New York: Maanillan, 1961. Sellars C M, Whiteman A. Recrystallization and Grain Growth in Hot Rolling [J]. Met Science, 1979, 13: 187. Maccagno T M, Jonas J J , Hodgson P D. Spreadsheet Modeling of Grain Size Evolution During Rod Rolling [J]. ISIJ Int, 1996, 36(6): 720. Fulvio Siciliano J r , Jonas J J. Mathematical Modeling of the Hot Strip Rolling of Microalloyed Nb, Multiply-Alloyed CrMo, and Plain C-Mn Steels [J]. Metall Mater Trans, 2000, 31A(2): 511. Hodgson P D, Gibbs R K. A Mathematical Model to Predict the Mechanical Properties of Hot Rolled C-Mn and Microalloyed Steels [J]. ISIJ Int, 1992, 32(12): 1329.