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Process Time Reduction by Means of Integrated Casting and Rolling
Process Time Reduction by Means of Integrated Casting and Rolling R. Kopp, Institute for Metal Forming, Technical University of Aachen, Germany Submitted by E. Doege (1). Institute for Metal Forming and Metal-Forming Machine Tools, University of Hannover, Germany Received on January 3, 1996
Abstracf The paper discusses the pros and cons of a process shortening in terms of effectiveness and flexibility. A combined castinglmetal-forming process offers great potential for process shortening. This is documented in detail for the case of the dcuble-roller technique of steel strip manufacture. The interlinking of casting and forming provides an integrated analysis of the liquid pnase. the solidification process and the directlylinked forming operation which follows solidification. The paper describes various models and their application for the analysis of the process cycle and the resulting properties of the product. Close attention is also given to determining the high temperature yield stress and the heat transmission coefficient for this ultra-high temperature forming process.
Kevwords: process time reduction; casting-rolling; modelling
1. Advantages and disadvantages of process time reduction in terms of effectiveness and flexibility
The four main criteria for competitive production, namely costs, time. quality and environmental compatibility, all argue in favour of a systematic reduction in process time. The shorter a process, the less labour- and cost-intensive it will be. A shorter process means that a product is manufactured more quickly, a factor of considerable importance in view of enormous innovation pressures. A shorter process means that there are fewer opportunities for errors to creep in, allowing higher and more reproducible quality. And a shorter process is also a more environmentally compatible process, i.e. a process which uses less energy and produces less waste or scrap. In the final analysis, all these advantages lead to an increase efficiency of the process chain. These advantages are accompanied by certain drawbacks. The shorter the process, the fewer will be the opportunities for the engineer to influence the geometrical and mechanical properties of the product. Final properties must be attained in a few steps or even in a single step. Another substantial disadvantage of the shortened process is that a product line can no longer be subdivided. For example, a hot wide strip line can be used to manufacture a wide range of semi-finished products - an advantage which is no longer available with a greatly shortened process line. . .. -__. . -.. -. __ . . , k l q 1’: Hd ))ti?$. Tre3tn;e~, Cold F ~ i ‘1i; CiQ
The effectiveness E and the flexibility F of a process are therefore countercurrent criteria for a process time reduction. Process effectiveness may be defined as the ratio of form and properties in relation to the number of process steps. Process flexibility may be defined in terms of rnanufacturable end products in relation to the process stages. Fig. 1 plots these two curves in relation to the number of processes. A hot wide strip line is, for example, quite as justified for the manufacture of a wide range of semi-finished strip and sheet products as are the new shortened processes which are becoming familiar under such names as continuous strip production (CSP). inline strip production (ISP), continuous rolling (Conroll) or double roller (DR). Extreme process shortening can be achieved by introducing the OR process for steel strip manufacture. 2. Description of the double roller process
This process, in which the casting and forming stages are especially closely interlinked, is being developed in various places throughout the world, and will be described in greater detail below. The main features of a DR process may be illustrated by the laboratory plant installed at the IBF 161.
F m ~
Fig. 1: Process time reduction
Annals o f the ClRP Vol. 45/1/1996
Fig. 2: Principle of the double roller
221
The steel melt is cast via a tundish between two horizontal internally cooled rolls On the roll surfaces, the steel melt solidifies into shell strips, which are then joined in the narrowest working gap (Fig. 2). The strip is guided by a driver into a cooling section and is then coiled. The casting rate, the roll velocity, the roll gap, the forming force. the driver velocity. the cooling water volume and the coil velocity must be coordinated exactly. This requires an extremely complex control system to operate the extremely non-linear and time-variable process. Fig. 3 shows an example of force control for a DR process in a rolling-force Istrip-!hickness diagram. I
Effective striD width
/
In order to achieve a quality at least comparable to that of conventionally manufactured strip, the processdetermining variables must be adjusted to ensure homogeneous, constant solidification and cooling parameters over the entire width of the strip. This is the precondition for even shell grobeh and a homogeneous temperature distribution across the width in the jcining zone Cifferences in :emperatwe are seen as one of :he possible causes of crack formation 1101. As will be apparent from the photograph of the emerging strip (Fig. 4). these requirements are not always satisfied. Clearly evident in the produced strip is a striped configuration with "hot" and "cold" zones. These temperature inhomogenities are primarily dependent on the complex interrelationships between the flow and temperature field caused in the melt pool by introduction of the melt and the roll geometry and forming processes in the roll gap. 4. Integrative analysis of the processes casting, solidification and forming
4.1 Modelling the temperature field in the melt and in the roll
Standard joperating point
/\ Thickness
Iiput strip thickness
Fig. 3: Force control principle of the double roller
3. Introduction to the problem
Fig. 4: A cast strip
222
Depending on the type and configuration of the prescribed inflow parameters. the introduction of melt to the pool induces characteristic melt flows, which influence the temperature field and hence solidification and cooling parameters through the mechanism of convective heat transport. In order to devise measures counteracting temperature inhomogeneities across the strip width. it is necessary to develop a process model describing the processes occurring in the pool and hence the formation of the strip. This model must include the flow in the melt, taking conductive and convective heat transport into account; it must also allow for the change in phase when the metal solidifies under the given process constraints. In order to investigate flow processes in the melt pool, water model studies were performed under similitude laws. Accompanying simulations with the PHOENICS FVM programme nl, using the K-& turbulence model 151, showed good correlation with the experimental results 141. The basic equations used to calculate the velocity and temperature distribution are the continuity, momentum and energy conservation equations Apart from these conservation equations, a 1-phase mixing statement describing the heterogeneous state was used to determine the temperature field in the double roller process 111. One set of conservation equations is valid for both phases throughout the computation zone. Phasedependent physical and material values in the heterogeneous zone are taken into account by the mixing values. The increase in flow resistance at the solidlliquid phase transition is allowed for by introducing suitable source terms in the momentum conservation equation, the permeability of the heterogeneous zone being formulated as a function of the solid fraction The analogy between dendritic solidification and flow in porous media leads to the use of DARCY's law 181. A large number of influencing factors with a wide range of different effects play a role during contact between two metallic surfaces 191. It is therefore necessary to couple the advance of the strip forming process with events at the rolllstrip-shell interface. The following sequence is probable and is illustrated in Fig. 5 141. The strip shell created in the upper meniscus range a) is extremely thin and adapts closely to the structure of the roll working
surface. This good contact entails an equally good heat flow, which cannot be simulated due to the short contact lenglh in this zone. As solidification and cooling continue, the strip shell contracts (zone b)), very quickly leading to localized formation of a gap, which substantially reduces the heat flow I1 11. When the strip shells are joined (zone c)) in the melt pool, an increasing pressure builds up on the strip shells which have grown most strongly up to this point. locally improving the heat flow (enlarged contact area). In the forming m n e (zone d)). the heat flow therefore increases rapidly, since both the contact area and the contact parameters have suddenly improved.This model concept is reproduced as follows in the simulation. Depending on the temperature pertaining in the symmetry plane between the roils, the heat transmission coefficient at temperatures higher than T1iq is set at 5 kW/rn2K (determined by heat transmission) and is then increased exponentially from 5 kWlm2K to 500 kW/m2K between Tliq and IT ,, (determined by heat conduction), in accordance with the curve shown in Fig. 5. The ratio of the two thermal resistances of the interface and strip shell (Biot factor) is also plotted.
p1 oooo.--
k
2
Y
.-
I
r
8
l
Ol OO-.
sol
T
_-
7
liq
Fig. 6: Calculated temperature distribution in the melt pool
I
1600 I
.
I
100
C
.-0 In .-In
i c
10
F c m I
0
I
___ 1400 "C 4
I
-.
~-
..
1435 "C
1470 'C
1505 "C
Temperature at strip centre ("C)
......
Fig. 5: Heat transmission coefficient curve The temperature field obtained with this model concept and satisfaction of the thermal balance is shown in Fig. 6 (Ti,, = 1600 C". Tliq = 1470 C".TsOl = 1435 C").The result is a visibly enlarged molterr zone. The effects of the inflowing melt on the strip formation process are clearly apparent. A consideration of individual temperature curves from the symmetry plane between the rolls (Fig. 7) indicates that relatively small local temperature differentials of some 20 K (25 mm ahead of the working gap) are by no means inconsistent with pronounced temperature gradients further down in the strip. This process, which is self-reinforcing, shows that significant gradients can arise from small temperature inhomogeneities in the strip shell zone. Since simulation results at this point also need to be compared with experimental data, a number of temperature measurements were made in the melt pool /4/. The small temperature differentials in the top zone of the pool are typical. It is also apparent that melt overheating following entry to the pool is dissipated relatively quickly to a uniform molten level. The entire overheating and solidification heat is dissipated via the cooling rolls; their distribution is in turn influenced by the prevailing solidification parameters (Fig. 8).
r-
0
10
.-.. -
.
.
.
30 40 50 60 Half pool width (mm)
20
-.70
Fig. 7: Calculated temperature curve in the symrnetrie plane between the rolls
..-
0 -.-6
._
.
-
0,5 E E a 0,4
A
.-C
b 0,3
n E
s
0.2
8
0.1
-
'
___ I
0
0
90
180
__ - .. 270
Circumference (Degree)
I
-
.-
360
Fig. 8: Roll cambering over the circumferences with variation of strip thickness
223
To describe strip formation it is necessarj to consider the geometry of the roll system as well as the heat transmission. The rolls expand due to heating, but must form the strip in the gap zone, to geometricaily close tolerances. In order to investigate the behaviour of the roll shell. FEM simulations were used to calculate mechanical stresses and the resulting expansions. In practice, roll cambering is compensated by suitable roll grinding. keeping the roll gap parallel at operating temperarurp. The cambering, shown over the roll circumference, changes its magnitude with the temperature gradient in the roll shell. The gradient and hence the cambering increase in the contact zone with the strip, falling again during the cooling phase. Cambering is greater if the strip thickness increases for a constant casting power i2l.
4.2 Description of the forming zone Theoretical considerations based on the ,:;-a lw for the determination of the input strip thickness s: 131 lead to the relationship /
I
where c is the solidification coefficient, n the solidification exponent. v the roll circumferential speed and 1, the time required for overheating to dissipate. In order to obtain an approximate simulation of the forming zone. it is necessary to know the hightemperature yield stress. Comparative studies were carried out at the IBF on the known method of determining yield stress by means of cylindrical upsetting tests and indentation tests. The upsetting test provides the yield stress values up to temperature TsOl. Indentation tests can be made even at higher specimen temperatures ( Z Tliq). and provide the yield resistance. Investigations have shown that. for the same specimen temperature, the proportionality factor for yield stress (upsetting test) and yield resistance (indentation test) follows a relatively constant curve up to solidus temperature (Fig. 9). and is independent of the forming rate 800
-..:. ,,
I I
-
600 1
E E 11)
II)
i
.
I
,!
max.striiiindentation
flow stress (upsetting test)
i
1: -
v
indentation test 400 -
5. Conclusions The double-roller process is a technique which closely interlinks the casting and forming stages Casting and solidification phenomena have a direct Influence on the forming processes which take place in the same roll set. The PHOENICS FVM programme was used to describe the flow, temperature and solidification parameters. The heat transmission conditions were approximated in accordance with the varying melffshell contact parameters. Using this model, it was possible to describe the phenomenon of temperature inhomogeneities in the emerging strip. It was shown that this process is selfreinforcing. Temperature inhomogeneities in the melt pool should therefore be eliminated as far as possible in order to achieve homogeneous strip properties. A complete understanding of the process is possible if the forming phenomena can also be simulated. This requires a knowledge of the high-temperature yield stress curve. A special apparatus capable of determining this variable was developed and demonstrated. The roll geometry has a substantial influence on mechanical properties, and must be dimensioned in accordance with temperature and pressure conditions. The resulting cambering due to the temperature distribution in the roll gap and to cooling can be calculated using the FEM rnefhod. Acknowledgements
.
solidus state
I
Pssurning a constant proportionality factor curve above the snlidus temperature, yield stresses above the solidus temperatiire can be calculated by multiplying the forming resistance by this factor. The resulting yield stress is no longer a yield stress in the strict sense of the term, but allows a rough simulation of the material flow in the sernisolidified state. The cooling rates of the apparatus integrated in a servohydraulic testing machine are abcut 200-300 Ks. The force values can be registered up to 35 kN. with a resoluticn of 0.1 N. The forming rate attainable with the given specimen geometries is 150 1:s ar a strain of 1. This apparatus is therefore capable of tracking !he process parameters occurring in the DR process to the correct order of magnitude For the future. this will provide a means of determining the high temperature yield curves required for an approximate simulation of material flows in the double roller process
:: flow stress
Sincere thanks are due to 0ipl.-lng Albrecht-Fruh, Dipl.-lng. Hentschel and Dipl.-lng. Heunen for their contribution in preparing this paper and their helpful suggestions. References 111
(extrapol.) . .... .. . . . . I
121
proportionalfactor -.
250
-
550 350 450 Temperature ('C)
700 AA 2024 (refined)
Fig. 9: Determining the high temperature yield stress
224
131
Benon, W. D.; Incropera. F. P.: A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems - 1/11. Model forrnulation; Inl. J. Heat Masslransfer, Vol. 30. No. 10, pp. 2161-2187, 1987 Beyer-Steinhauer. H.: Thermische Walzenbombierung beim Zwei-RollenGieRwalzverfahren; Umformtechnische Schriften, Band 39, Verlag Stahleisen Dusseldorf. 1993 Hirt G: Beitrag zur Auslegung und Simulation von Gieflwalzprozessen: Umformtechnische Schriften. Band 36, Verlag Stahleisen Dusseldorf. 1988
I4I
151
161
191
I101
I1 11
Jestrabek, J.. S;ahlbandherslellung nach den1 Zweirollenverfahren - MDdellierung des Strornungs und Ternperaturfeldes; Urnforrntechnische Schriften. Band 55, Verlag Stahleisen Dusseldorf, 1995 Launder, B.E.; D.B. Spalding: The Nurnrnerical Cornpulalior. of Turbulenz FIows Cornptiter Methods in Applied Mechanics and Engeneering 3.Ncrth-Holland Publishing Company 1974 Litterscheidt. H.; Hammer. I?.:Schneider. C . ; Simon. R . W : Senk.D.; Kopp, R.: Henl. 3.: Bandgienen nach dem Zweircllenverfahren Stand der Entwickiung bei cer Thyssen Stahl AG; Stahl und Eisen 111 (1991). Nr.2. S 61-66 Ludwig, J.C.: Quin. H.Q.: Scalding. E.B.: Tire PHOENICS Reference Manual, Version 1.5.3. 1989 Ohnaka, I.; Kobayashi. K.: Flow Analysis during Solidification by the Direct Finite Difference Method: Transactions ISIJ. Vol. 26. 1986 Schrnitz. W.: Beitrag zurn endabrnessungsnahen Glenen dunner Stahlbander nach dem Zweirollenverfahren; Dissertation RWTH Aachen 1991 Tagungsbericht : "Endabrnessungsnahes Gienen". ScottsdalelAz., USA: Feb. 1993: Bandgienen - die Zukunft bleibt offen; Stahl und Eisen 113 (1993) Nr. 5, S. 1211124. von Kiss, M.: Der Warmeubergang zwischen sich beruhrenden metallischen Oberflachen; NeueTechnik 5. S.714-724, 1963
225
Abstracf The paper discusses the pros and cons of a process shortening in terms of effectiveness and flexibility. A combined castinglmetal-forming process offers great potential for process shortening. This is documented in detail for the case of the dcuble-roller technique of steel strip manufacture. The interlinking of casting and forming provides an integrated analysis of the liquid pnase. the solidification process and the directlylinked forming operation which follows solidification. The paper describes various models and their application for the analysis of the process cycle and the resulting properties of the product. Close attention is also given to determining the high temperature yield stress and the heat transmission coefficient for this ultra-high temperature forming process.
Kevwords: process time reduction; casting-rolling; modelling
1. Advantages and disadvantages of process time reduction in terms of effectiveness and flexibility
The four main criteria for competitive production, namely costs, time. quality and environmental compatibility, all argue in favour of a systematic reduction in process time. The shorter a process, the less labour- and cost-intensive it will be. A shorter process means that a product is manufactured more quickly, a factor of considerable importance in view of enormous innovation pressures. A shorter process means that there are fewer opportunities for errors to creep in, allowing higher and more reproducible quality. And a shorter process is also a more environmentally compatible process, i.e. a process which uses less energy and produces less waste or scrap. In the final analysis, all these advantages lead to an increase efficiency of the process chain. These advantages are accompanied by certain drawbacks. The shorter the process, the fewer will be the opportunities for the engineer to influence the geometrical and mechanical properties of the product. Final properties must be attained in a few steps or even in a single step. Another substantial disadvantage of the shortened process is that a product line can no longer be subdivided. For example, a hot wide strip line can be used to manufacture a wide range of semi-finished products - an advantage which is no longer available with a greatly shortened process line. . .. -__. . -.. -. __ . . , k l q 1’: Hd ))ti?$. Tre3tn;e~, Cold F ~ i ‘1i; CiQ
The effectiveness E and the flexibility F of a process are therefore countercurrent criteria for a process time reduction. Process effectiveness may be defined as the ratio of form and properties in relation to the number of process steps. Process flexibility may be defined in terms of rnanufacturable end products in relation to the process stages. Fig. 1 plots these two curves in relation to the number of processes. A hot wide strip line is, for example, quite as justified for the manufacture of a wide range of semi-finished strip and sheet products as are the new shortened processes which are becoming familiar under such names as continuous strip production (CSP). inline strip production (ISP), continuous rolling (Conroll) or double roller (DR). Extreme process shortening can be achieved by introducing the OR process for steel strip manufacture. 2. Description of the double roller process
This process, in which the casting and forming stages are especially closely interlinked, is being developed in various places throughout the world, and will be described in greater detail below. The main features of a DR process may be illustrated by the laboratory plant installed at the IBF 161.
F m ~
Fig. 1: Process time reduction
Annals o f the ClRP Vol. 45/1/1996
Fig. 2: Principle of the double roller
221
The steel melt is cast via a tundish between two horizontal internally cooled rolls On the roll surfaces, the steel melt solidifies into shell strips, which are then joined in the narrowest working gap (Fig. 2). The strip is guided by a driver into a cooling section and is then coiled. The casting rate, the roll velocity, the roll gap, the forming force. the driver velocity. the cooling water volume and the coil velocity must be coordinated exactly. This requires an extremely complex control system to operate the extremely non-linear and time-variable process. Fig. 3 shows an example of force control for a DR process in a rolling-force Istrip-!hickness diagram. I
Effective striD width
/
In order to achieve a quality at least comparable to that of conventionally manufactured strip, the processdetermining variables must be adjusted to ensure homogeneous, constant solidification and cooling parameters over the entire width of the strip. This is the precondition for even shell grobeh and a homogeneous temperature distribution across the width in the jcining zone Cifferences in :emperatwe are seen as one of :he possible causes of crack formation 1101. As will be apparent from the photograph of the emerging strip (Fig. 4). these requirements are not always satisfied. Clearly evident in the produced strip is a striped configuration with "hot" and "cold" zones. These temperature inhomogenities are primarily dependent on the complex interrelationships between the flow and temperature field caused in the melt pool by introduction of the melt and the roll geometry and forming processes in the roll gap. 4. Integrative analysis of the processes casting, solidification and forming
4.1 Modelling the temperature field in the melt and in the roll
Standard joperating point
/\ Thickness
Iiput strip thickness
Fig. 3: Force control principle of the double roller
3. Introduction to the problem
Fig. 4: A cast strip
222
Depending on the type and configuration of the prescribed inflow parameters. the introduction of melt to the pool induces characteristic melt flows, which influence the temperature field and hence solidification and cooling parameters through the mechanism of convective heat transport. In order to devise measures counteracting temperature inhomogeneities across the strip width. it is necessary to develop a process model describing the processes occurring in the pool and hence the formation of the strip. This model must include the flow in the melt, taking conductive and convective heat transport into account; it must also allow for the change in phase when the metal solidifies under the given process constraints. In order to investigate flow processes in the melt pool, water model studies were performed under similitude laws. Accompanying simulations with the PHOENICS FVM programme nl, using the K-& turbulence model 151, showed good correlation with the experimental results 141. The basic equations used to calculate the velocity and temperature distribution are the continuity, momentum and energy conservation equations Apart from these conservation equations, a 1-phase mixing statement describing the heterogeneous state was used to determine the temperature field in the double roller process 111. One set of conservation equations is valid for both phases throughout the computation zone. Phasedependent physical and material values in the heterogeneous zone are taken into account by the mixing values. The increase in flow resistance at the solidlliquid phase transition is allowed for by introducing suitable source terms in the momentum conservation equation, the permeability of the heterogeneous zone being formulated as a function of the solid fraction The analogy between dendritic solidification and flow in porous media leads to the use of DARCY's law 181. A large number of influencing factors with a wide range of different effects play a role during contact between two metallic surfaces 191. It is therefore necessary to couple the advance of the strip forming process with events at the rolllstrip-shell interface. The following sequence is probable and is illustrated in Fig. 5 141. The strip shell created in the upper meniscus range a) is extremely thin and adapts closely to the structure of the roll working
surface. This good contact entails an equally good heat flow, which cannot be simulated due to the short contact lenglh in this zone. As solidification and cooling continue, the strip shell contracts (zone b)), very quickly leading to localized formation of a gap, which substantially reduces the heat flow I1 11. When the strip shells are joined (zone c)) in the melt pool, an increasing pressure builds up on the strip shells which have grown most strongly up to this point. locally improving the heat flow (enlarged contact area). In the forming m n e (zone d)). the heat flow therefore increases rapidly, since both the contact area and the contact parameters have suddenly improved.This model concept is reproduced as follows in the simulation. Depending on the temperature pertaining in the symmetry plane between the roils, the heat transmission coefficient at temperatures higher than T1iq is set at 5 kW/rn2K (determined by heat transmission) and is then increased exponentially from 5 kWlm2K to 500 kW/m2K between Tliq and IT ,, (determined by heat conduction), in accordance with the curve shown in Fig. 5. The ratio of the two thermal resistances of the interface and strip shell (Biot factor) is also plotted.
p1 oooo.--
k
2
Y
.-
I
r
8
l
Ol OO-.
sol
T
_-
7
liq
Fig. 6: Calculated temperature distribution in the melt pool
I
1600 I
.
I
100
C
.-0 In .-In
i c
10
F c m I
0
I
___ 1400 "C 4
I
-.
~-
..
1435 "C
1470 'C
1505 "C
Temperature at strip centre ("C)
......
Fig. 5: Heat transmission coefficient curve The temperature field obtained with this model concept and satisfaction of the thermal balance is shown in Fig. 6 (Ti,, = 1600 C". Tliq = 1470 C".TsOl = 1435 C").The result is a visibly enlarged molterr zone. The effects of the inflowing melt on the strip formation process are clearly apparent. A consideration of individual temperature curves from the symmetry plane between the rolls (Fig. 7) indicates that relatively small local temperature differentials of some 20 K (25 mm ahead of the working gap) are by no means inconsistent with pronounced temperature gradients further down in the strip. This process, which is self-reinforcing, shows that significant gradients can arise from small temperature inhomogeneities in the strip shell zone. Since simulation results at this point also need to be compared with experimental data, a number of temperature measurements were made in the melt pool /4/. The small temperature differentials in the top zone of the pool are typical. It is also apparent that melt overheating following entry to the pool is dissipated relatively quickly to a uniform molten level. The entire overheating and solidification heat is dissipated via the cooling rolls; their distribution is in turn influenced by the prevailing solidification parameters (Fig. 8).
r-
0
10
.-.. -
.
.
.
30 40 50 60 Half pool width (mm)
20
-.70
Fig. 7: Calculated temperature curve in the symrnetrie plane between the rolls
..-
0 -.-6
._
.
-
0,5 E E a 0,4
A
.-C
b 0,3
n E
s
0.2
8
0.1
-
'
___ I
0
0
90
180
__ - .. 270
Circumference (Degree)
I
-
.-
360
Fig. 8: Roll cambering over the circumferences with variation of strip thickness
223
To describe strip formation it is necessarj to consider the geometry of the roll system as well as the heat transmission. The rolls expand due to heating, but must form the strip in the gap zone, to geometricaily close tolerances. In order to investigate the behaviour of the roll shell. FEM simulations were used to calculate mechanical stresses and the resulting expansions. In practice, roll cambering is compensated by suitable roll grinding. keeping the roll gap parallel at operating temperarurp. The cambering, shown over the roll circumference, changes its magnitude with the temperature gradient in the roll shell. The gradient and hence the cambering increase in the contact zone with the strip, falling again during the cooling phase. Cambering is greater if the strip thickness increases for a constant casting power i2l.
4.2 Description of the forming zone Theoretical considerations based on the ,:;-a lw for the determination of the input strip thickness s: 131 lead to the relationship /
I
where c is the solidification coefficient, n the solidification exponent. v the roll circumferential speed and 1, the time required for overheating to dissipate. In order to obtain an approximate simulation of the forming zone. it is necessary to know the hightemperature yield stress. Comparative studies were carried out at the IBF on the known method of determining yield stress by means of cylindrical upsetting tests and indentation tests. The upsetting test provides the yield stress values up to temperature TsOl. Indentation tests can be made even at higher specimen temperatures ( Z Tliq). and provide the yield resistance. Investigations have shown that. for the same specimen temperature, the proportionality factor for yield stress (upsetting test) and yield resistance (indentation test) follows a relatively constant curve up to solidus temperature (Fig. 9). and is independent of the forming rate 800
-..:. ,,
I I
-
600 1
E E 11)
II)
i
.
I
,!
max.striiiindentation
flow stress (upsetting test)
i
1: -
v
indentation test 400 -
5. Conclusions The double-roller process is a technique which closely interlinks the casting and forming stages Casting and solidification phenomena have a direct Influence on the forming processes which take place in the same roll set. The PHOENICS FVM programme was used to describe the flow, temperature and solidification parameters. The heat transmission conditions were approximated in accordance with the varying melffshell contact parameters. Using this model, it was possible to describe the phenomenon of temperature inhomogeneities in the emerging strip. It was shown that this process is selfreinforcing. Temperature inhomogeneities in the melt pool should therefore be eliminated as far as possible in order to achieve homogeneous strip properties. A complete understanding of the process is possible if the forming phenomena can also be simulated. This requires a knowledge of the high-temperature yield stress curve. A special apparatus capable of determining this variable was developed and demonstrated. The roll geometry has a substantial influence on mechanical properties, and must be dimensioned in accordance with temperature and pressure conditions. The resulting cambering due to the temperature distribution in the roll gap and to cooling can be calculated using the FEM rnefhod. Acknowledgements
.
solidus state
I
Pssurning a constant proportionality factor curve above the snlidus temperature, yield stresses above the solidus temperatiire can be calculated by multiplying the forming resistance by this factor. The resulting yield stress is no longer a yield stress in the strict sense of the term, but allows a rough simulation of the material flow in the sernisolidified state. The cooling rates of the apparatus integrated in a servohydraulic testing machine are abcut 200-300 Ks. The force values can be registered up to 35 kN. with a resoluticn of 0.1 N. The forming rate attainable with the given specimen geometries is 150 1:s ar a strain of 1. This apparatus is therefore capable of tracking !he process parameters occurring in the DR process to the correct order of magnitude For the future. this will provide a means of determining the high temperature yield curves required for an approximate simulation of material flows in the double roller process
:: flow stress
Sincere thanks are due to 0ipl.-lng Albrecht-Fruh, Dipl.-lng. Hentschel and Dipl.-lng. Heunen for their contribution in preparing this paper and their helpful suggestions. References 111
(extrapol.) . .... .. . . . . I
121
proportionalfactor -.
250
-
550 350 450 Temperature ('C)
700 AA 2024 (refined)
Fig. 9: Determining the high temperature yield stress
224
131
Benon, W. D.; Incropera. F. P.: A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems - 1/11. Model forrnulation; Inl. J. Heat Masslransfer, Vol. 30. No. 10, pp. 2161-2187, 1987 Beyer-Steinhauer. H.: Thermische Walzenbombierung beim Zwei-RollenGieRwalzverfahren; Umformtechnische Schriften, Band 39, Verlag Stahleisen Dusseldorf. 1993 Hirt G: Beitrag zur Auslegung und Simulation von Gieflwalzprozessen: Umformtechnische Schriften. Band 36, Verlag Stahleisen Dusseldorf. 1988
I4I
151
161
191
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