INFLUENCE OF UNDERCOOLED SURFACE OF CCSP ON CORE PROPAGATION OF PLASTIC DEFORMATION. Richard Fabík a Jiří Kliber a

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1 INFLUENCE OF UNDERCOOLED SURFACE OF CCSP ON CORE PROPAGATION OF PLASTIC DEFORMATION. Richard Fabík a Jiří Kliber a a SB-Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, Department of Materials Forming, 17. listopadu 15, Ostrava-Poruba, Czech Republic, richard.fabik@vsb.cz jiri.kliber@vsb.cz Abstract The presented paper describes computer simulation of the square billet rolling from the input round semi-product. The influence of undercooled surface layers of continuously cast semi-product on the propagation of the plastic deformation to the core of the rolled product was investigated via PC simulation. The simulation was performed with 2D FormFEM 1.5 simulation program of forming processes. The employed method of design can be called 2,5D, i.e. simulation of metal flow in the plane of rolling only, with cross section reduction according to the actual elongation coefficient. Simulation results (for all 17 passes and 4 degrees of undercooling of surface) are as follows: stress intensity field, dependence of temperature on a distance from the core to the surface for x and y axis, strain intensity dependence on a distance from the core to the surface for x and y axis. Our presumption, that alternative cross section behaviour of deformation resistance caused by undercooled surface results in alternation of strain intensity distribution, was confirmed (higher value of strain in the core was observed in the undercooled surface). 1. INTRODUCTION The main objective of the project was performance of the computer simulation of rolling the billet 285 x 285 mm from CCSP (continuously cast semi-product) of the initial diameter of 525 mm. The occurrence of internal defects during ultrasound defectoscopy in the core areas led us to believe that during rolling, due to a low level of strain, a sufficient throughforming of the core areas is not experienced. During PC simulation an influence of CCSP surface layers cooling on propagation of the plastic deformation to the core of the rolled product, was monitored. For that purpose, simulation of CCSP cooling was made. Simulation of rolling was then performed at four temperature levels of the surface ranging from 1300 to 1000 C, which resulted in a different course of temperature dependence upon the distance from the CCSP core. 2. PROGRAM FOR SIMULATION OF FORMING OPERATIONS WITH THE METHOD OF FINITE ELEMENTS FORMFEM 2.1 General characteristics The program uses rigid-plastic formulation of the Method of Finite Elements represented by the σ δ & ε d + σ d + d mδε& δσ & mε S F Fiδu ids = 0, (1) where σ stress intensity 1

2 σ m middle (hydrostatic) stress ε& strain volume rate ε&. strain rate. The condition of incompressibility & ε = & ε1 + & ε 2 + & ε3 = 0 met via the method of Lagrange multipliers [1]. The material does not feature elastic properties, which is limiting the applied equation at high temperatures, or at situations, where elastic strains are negligible when compared with plastic ones. The temperature modules are based on Furier equation, which is solved separately from the mechanical part. The temperature link is performed by iteration way. The temperature module enables determination of the temperature field both in formed bodies, and in tools. The link of mechanic and temperature model is made via the member σ εdv & = q, representing quantity of heat established in the formed body as a consequence of forming activity. The calculation employs the adhesion friction model. 3. DESIGN Design itself consists of two parts: 1. Simulation of cooling resulting in the time course of the heat field of CCSP, which was used as an input information for simulation of rolling. 2. Simulation of rolling performed with 2.5D simulation for all 17 passes (and two temperature fields) on the basis of empirical knowledge of the coefficient of elongation. 3.1 Simulation of cooling The FormFEM program [2-3] enables user on the basis of a specified chemical composition of steel to calculate the following properties in dependence on temperature: specific heat, density, thermal conductivity. Graphic curves are illustrated in Fig For simulation, steel of the basic chemical composition of the following weight percentage was used - C-0,35; Mn-0,7; Si-0,30; Cr max 0,25; Ni max. 0,30; Cu max. 0,30; S max. 0,040; P- max. 0,040. Fig. 1. Specific heat as a function of temperature Fig. 2. Density as a function of temperature 2

of coefficient of heat transfer. The Calculation respects the equation entered in the internal structure of the FormFEM programme.

3 Fig. 3. Conductivity as a function of temperature Fig. 4. Temperature field at cooling of CCSP of the diameter of 525 mm for various times (45, 90, 180, 300 s) An example of CCSP cooling was designed as an open air cooling using automatic calculation of coefficient of heat transfer. The Calculation respects the equation entered in the internal structure of the FormFEM programme. The task was solved in this part as a symmetric one according to x and y axis to avoid problems caused by a small number of contact points between the roller and semi-product at the beginning of simulation of rolling. More information about 2.5D method is included in the following chapter. The resulting temperature field for cooling times of 45, 90, 180, 300 s are is shown in Fig. 4. 3

3.2 Simulation of rolling 3.2.1 Simulation with 2.5 D method Rolling is a process which is running at three dimensions. As the 2.

metal flow only at the plane of rolling, while cross-section of the semi-product is reduced at the start of simulation by the value resulting from the measured coefficient of elongation.

4 3.2 Simulation of rolling Simulation with 2.5 D method Rolling is a process which is running at three dimensions. As the 2.5D programme of simulation is available for us, we applied a method of design which could be called with a certain bit of exaggeration 2.5D. The principle of the method consists in simulation of metal flow only at the plane of rolling, while cross-section of the semi-product is reduced at the start of simulation by the value resulting from the measured coefficient of elongation. After completion of modelling of a single pass, the resulting geometry and temperature field of the rolled product transferred to the next operation (see section 2.2 the programme structure) is again reduced according to the value of coefficient of elongation from the next pass (note: the field of deformations is not transported between passes, we assume the total recovery of the structure in time between passes). This design suggests certain mispresentation of results, however, for comparison of rolling under different conditions it is very much convenient Establishment of the set and limit conditions of the task The task had to be split into two areas due to the programme limitations (10 operations per issue). For each of 17 passes an operation was established containing 4 (first three passes), eventually 2 sets for a different temperature field. Fig. 5. shows the final elements grid and the initial conditions of the semi-product including tools for the set No. 1 (cooling time 300 s, see Fig. 4.) operation 1. (1st pass). Fig. 6. shows the set 1 of the initial temperature field. Fig. 5. Finite elements grid and limit conditions Fig. 6. A set with temperature field Boundary and initial conditions: Contact conditions: friction: µ = 0,6; heat transfer: α = Wm -1 K -1 Condition of heat transfer: air calculation, T = 20 C, ε = 0,8 Initial temperatures: roll: 20 C, semi-product: result of previous step Material: roll: heat properties: λ = 36,5 Wm -1 K -1 ; ρ = kgm -3 ; C = 494 Jkg -1 K -1 mechanical properties: non-deformable object Move of tool: linear, speed of: 250 mms -1 Constitutive equation: m 2 m3 m 9 σ f = A T ε & ε (2) Kde A = 4, ; m 2 = -3,51941; m 3 = 0,181389; m 9 = 0,14681, Graphic illustration see Fig. 7. 4

5 3.3 Results Temperature ( C) Intensity of strain (-) Fig. 7. Stress-strain curves strain depending on temperature (1000 to 1300 C) The results of simulation are: Dependence of temperature on a distance from the core to the axes x and y for all 17 passes (Fig. 8.) Dependence of intensity of strain on a distance from the core for the axes x and y for all 17 passes (Fig. 8.) ,14 0,12 0,1 0,08 0,06 0,04 0, C 1150 C 1100 C 1000 C x-axis Distance from the Core (mm) 1300 C 1150 C 1100 C 1000 C y-axis Distance from the Core (mm) Temperature ( C) Intensity of strain (-) As it has been already stated above, 4 sets were established ( for temperature field see Fig. 4.), identification in graphs according to surface temperature T at the start of simulation: Set 1 cooling time t = 300s, T = C, passes 1 to 17. Set 2 cooling time t = 90s, T = C, passes 1 to 3. Set 3 cooling time t = 45s, T = C, passes 1 to 3. Set 4 cooling time t = 0s, T = C, passes 1 to ,12 0,1 0,08 0,06 0,04 0, C 1150 C 1100 C 1000 C Fig. 8. Results after the first pass y-axis Distance from the Core (mm) x-axis 1300 C 1150 C 1100 C 1000 C Distance from the Core (mm)

6 Fig. 8. shows results after the first pass in the following sequence: Temperature as a function of a distance from the core of axis x, axis y; Intensity of strain as a function of a distance from the core, axis x, axis y. The graphs of dependence of intensity of deformation on a distance from the centre are of the best illustrative capacity. These results are summarized in Table 1, suggesting the following: Due to cooling of surface layers intensity of deformation will increase in the centre of the semi-product by 17 %. This increase is evident in all passes except for 1st and 2nd. In those passes, maximum of intensity of strain balances at a distance about 140 to 150 mm from the core and that value is bigger than in case of temperature of the surface C. As regards to the difference in percentage, the most significant are the passes 4., 6. and 14., where a difference between the cooled and non-cooled semi-product exceeds 27 %. A big difference in the last 17 th pass (over 160 %) is caused by inaccuracies at the change of cross section (see section Simulation by the 2.5D method) and the change of the strain level resulting from it. That problem has been already solved with the programme designers. Table 1. Maximum values of intensity of strain for individual passes Pass Strain (-) Strain (-) Distance Distance Initial surface Difference Initial surface Difference from the Pass from the core (mm) temperature ( C) core (mm) temperature ( C) % % ,121 0,132 9, ,115 0,125 8, ,098 0,097-1, ,245 0,297 21, ,158 0,148-6, ,196 0,225 14, ,313 0,316 0, ,158 0,187 18, ,170 0,217 27, ,169 0,205 21, ,180 0,200 11, ,262 0,335 27, ,175 0,225 28, ,253 0,282 11, ,130 0,152 16, ,143 0,157 9, ,177 0,228 28, ,031 0, ,516 At this point it is necessary to stress that the main parameter used for set up of simulation was the value of elongation (eventually the length of the semi-product after the pass l 1 ), having been a part of specification. Moreover, the fact, that the actual volume at the start of rolling (circle area x length) is smaller by 3.5 % than the actual volume at the end of rolling (circle area without consideration of edges round off x length, is worth to be paid attention. As an example, two pictures are presented showing propagation of plastic deformation to the core, namely at the passage No. 5. Fig. 9. illustrates an example of the set 1, where for simulation, temperature on the surface was chosen to be T = 1000 C cooling time t = 300s and Fig. 10. shows the case of the Set 4, where for simulation, temperature on the surface was chosen to be T = 1300 C cooling time t = 0s [4]. 4. CONCLUSION On the basis of the performed simulation we have arrived at a series of the following conclusions: 1. The selected methodology of simulation of the course of the temperature field performed by the stated programme appears to be convenient and reliable. Should more precise attempt be required, it would be necessary to perform very costly and comprehensive tests 6

with bored in thermocouples, eventually use experience of other designers in the area of temperature fields.

Pass 5, Set 4; cooling time t = 300s, T = 1 000 C t = 0s, T = 1 300 C Fig. 11. Pass 10, Set 1; cooling time Fig. 12. Pass 10, Set 4; cooling time t = 300s, T = 1 000 C t = 0s, T = 1 300 C 2.

5D which is quite unique and not used elsewhere, enabling 2D area simulation of space forming even in shaped gauges at rolling, is relatively cheap (as opposed to the full value 3D programme), but

It is understandable, that the lower level of accuracy, a series of simplifications, necessity of a sensible estimation and the significant level of labour developed at a specific solution, are of

It is mainly the issue of homogeneity of the input temperature after cross section as a boundary condition, which is crucial.

7 with bored in thermocouples, eventually use experience of other designers in the area of temperature fields. As the programme FormFem itself was verified prior to application, the obtained data can be considered as reliable ones. Fig. 9. Pass 5, Set 1; cooling time Fig. 10. Pass 5, Set 4; cooling time t = 300s, T = C t = 0s, T = C Fig. 11. Pass 10, Set 1; cooling time Fig. 12. Pass 10, Set 4; cooling time t = 300s, T = C t = 0s, T = C 2. We managed to debug constants of input boundary conditions. 3. The method called 2.5D which is quite unique and not used elsewhere, enabling 2D area simulation of space forming even in shaped gauges at rolling, is relatively cheap (as opposed to the full value 3D programme), but sufficiently reliable method. It is understandable, that the lower level of accuracy, a series of simplifications, necessity of a sensible estimation and the significant level of labour developed at a specific solution, are of disadvantage. In the course of design a contact with the programme designers was established and knowledge was handed over with the objectives of improvement of certain data transfer in passes. 4. It is mainly the issue of homogeneity of the input temperature after cross section as a boundary condition, which is crucial. In total, three options may be expected: - charge of continuously cast semi-products into the furnace of minimum final heat; at this point it can be speculated, that a temperature in the core can be higher than practically measured and expected after heating in the furnace on the surface (let s say those 1300 C), then we can experience a paradoxical situation, when theoretically and practically plasticity can exceed the peak of formability and eventual internal defects may result from such influence; - homogenous temperature after cross section, which was our specification, be obtained by any combination of time after cast, temperatures and the time of dwell in the furnace charge of cold heat and imperfect heating of the core, which is very negative, as results will suggest. 7

8 5. Basic output of the work is confirmation of presumption, that undercooled surface, thus a different course of the strain resistance into nucleus with mild increase of this value to the surface (dependence of strain resistance on temperature is exponential, but in the limited range between 1300 to 1000 C this increase is relatively low) results in a different course of strain to the core. During a short pause, i.e. at the start of rolling, immediately at the same temperature levels of the surface and the centre (Set 4) the propagation of plastic deformation into the centre is lower than in Set 1, when by cooling during 300 s resulted in drop of temperature on the surface to 1000 C and in negligible drop in the centre of the semi-product. The course shown in Fig Fig. 12. may be a typical one, where the area of intense deformation in the centre - Fig. 10 (Fig. 12.) is, as opposed to Fig. 9. (Fig.11.), significantly lower. Other attachments are not so dramatic, but the trend is clear. The sets 2 and 3, which represented cooling of the surface to 1150, event. to 1100 C, reflect such trend as well. 6. The charts, which represent strain course in x and y axis, are conclusive as well as strain isolines. Also the trends of increased volume of strain intensity on the core for undercooled surface are evidence there. (See Fig. 11. and Fig. 12). Fig. 11. Dependence of intensity of strain on distance from the bar core, 4 pass, y axis Fig.12. Dependence of intensity of strain on distance from the bar core, 4 pass, x axis 7. So the final result suggests, that if the surface is undercooled, deformation is moving deeper to the core and it may be expected, that it will contribute in sealing of internal nonintegrity areas. ACKNOWLEDEGMENTS The present work performed within the framework of the research plan MSM MŠMT ČR. LITERATURE [1] LENARD, J.G., PIETRZYK, M., CSER, L. Mathematical and Physical Simulation of the Properties of Hot Rolled Products. Elsevier 1999, ISBN [2] FormFem Software for FEM simulation of forming, User s Guide, ITA, Ostrava, August [3] FABÍK, R., KLIBER, J. FormFem program pro simulaci tváření rovinných a rotačně symetrických těles, uživatelská příručka. Příloha k závěrečné zprávě grantového projektu MŠMT ČR FRŠ , Ostrava 2001, 56 s. [4] FABÍK, R., KLIBER, J. Závěrečná zpráva: PC simulace proniku plastické deformace do středu vývalku v závislosti na ochlazení povrchových vrstev při válcování sochoru 285 x 285 mm.šb-tu Ostrava,

THE INFLUENCE OF MN STEELS AGEING ON HEAT TRANSFER PHENOMENA. Eva Mazancová, Pavel Koštial, Ivan Ružiak, Milada Gajtanská, Ľuboš Krišťák *

THE INFLUENCE OF MN STEELS AGEING ON HEAT TRANSFER PHENOMENA Eva Mazancová, Pavel Koštial, Ivan Ružiak, Milada Gajtanská, Ľuboš Krišťák * Technical University of Ostrava, Faculty of Metallurgy and Material