FINITE ELEMENTS METHOD (FEM) SIMULATION OF BAR ROLLING IN OVAL - CIRCLE PASS SCHEDULE

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1 FINITE ELEMENTS METHOD (FEM) SIMULATION OF BAR ROLLING IN OVAL - CIRCLE PASS SCHEDULE Milan KOTAS a, Richard FABÍK b, Tomáš GAJDZICA a, Jiří KLIBER b a TŘINECKÉ ŽELEZÁRNY, a. s., Průmyslová 1000, Třinec, ČR, milan.kotas@trz.cz, tomas.gajdzica2@trz.cz, b FMMI, VŠB-TU Ostrava, 17. listopadu 15, Ostrava - Poruba, ČR, richard.fabik@vsb.cz, jiri.kliber@vsb.cz Abstract During practical experiments relating to thermomechanical rolling of steel bars on continuous fine section mill of Trinec Steelworks, non-homogenity of structure and significant difference in size of grain on bar crosssection were revealed. In relation to different structures and grain size, the resulting mechanical values of material are different in individual parts of the rolled product as well. Such differences are mostly unacceptable for the customers. The process of rolling of round bars is characterized by oval-circle pass schedule. The final set comprises two-high rolling mills in ASC system (Automatic Sizing Control). Uneven course of deformation across section of the rolled item during the rolling, which is a characteristic phenomenon in all working process, results in different course of strengthening and softening processes. Their kinetics depends on current deformation parameters, particularly temperature, equivalent strain and strain rate. 3D FEM rolling process simulation was performed for the selected final diameter, which is a true reflection of real operating conditions in ASC semi-finishing and finishing mill. Simulation was processed in FORGE application for medium-carbon steel C20. FEM simulation was used as an efficient tool for description of thermal-stress-deformation field across the rolling gap. The main attention was devoted to resulting course of strain rate, strain and temperature. Courses of values of these capacities were processed depending on position of the point of interest in the rolled item cross-section. The courses proved occurrence of nonhomogeneity of deformation parameters across the section, which is given by the applied production technology. Keywords: FEM simulation, bar rolling, recrystallization, strain rate, oval circle calibration 1. INTRODUCTION The experimental possibilities of following microstructural evolution in industrial bar mills at intermediate stages are very limited, because the difficulties in both cutting samples and quenching them in times short enough to freeze the austenitic microstructure. The alternative of reproducing industrial rolling conditions in pilot mills or plastometers is restricted because of their smaller geometric dimensions, their slower rolling speeds, lower strain rates and the absence of interstand tensions [1]. The presence of dynamic recrystallization (DRX) and metadynamic recrystallization (MDRX) in the finishing rod and bar rolling depends on the actual value of critical strain (ε c ) for the generation of dynamic recrystallization. According to general formula (1), the dynamic recrystallization is a function of strain rate, temperature and initial austenitic grain size [2] ε = c p q AZ d0 (1)

2 where A, p and q are constants, Z is Zener-Hollomon parameter and d 0 is the pre-recrystallization grain size. The TS bar mill is equipped with final ASC unit consisting of two duo mills with roll diameters of 300 mm. Based on the forming parameters achieved on the mills the DRX occurrence is expected during trial rolling at temperatures below 950 C. Some steel grades showed inhomogenity of grain size of the final ferritic structure over the rolled bar cross section. The inhomogenity can be caused by differences in DRX development during the passage through the ASC mills - see [1] and [3]. 2. EXPERIMENT In order to verify the hypothesis of the effect of different strain conditions on the inhomogenity of final structural properties of rolled bars on the ASC mills a computer simulation corresponding to the strain conditions on the mills was prepared. FORGE software enabling to employ the Finite Elements Method (FEM) was applied. An oval circle roll pass schedule is used in the ASC mills. The simulation is illustrated in Fig. 1. The programs incorporating FEM normally allow using the axial symmetry. In the present case the task is symmetrical with x and z axes. This will enable to take into account only a fourth of the rolled bar thereby remarkably reducing the Fig. 1. Configuration of rolls in ASC mill - FEM model calculation time [4]. The process of rolling to 20 mm final diameter from 25 mm initial diameter was simulated. The initial rolled bar temperature was 850 C and the temperature of rollers was 40 C. The final rolling velocity was 10 m/s. The material properties of the deformed material were sourced from the FORGE rheology database. They correspond to C20 steel, i.e. C = 0.18 %, Mn = 1.3 % and Si = 0.2 %. The mill roll axial distance is 3.5 m. The diagrams of the final distribution of strain intensities for the passage through the leader ASC mill and finishing mill are shown in Fig. 2. and Fig. 3., respectively. The nonuniformity of strain intensity distribution is clearly shown. It results from the applied rolling method in the oval round schedule. In case of the outlet level of leader mill rolls (Fig. 2.) the values range from Se = 0.25 at the extreme rolled bar spread point to 0.65 at the rolled bar centre. In the output level of the finisher (Fig. 3.) we can find two areas of the max. equivalent strain, in the center of the shaped part (Se = 1.23) and on the surface in the direction [101] (Se = 1.2). Between those places the deformation field is quite homogenous with the lowest value Se = c However, the areas with the minimum value of equivalent strain are quite more interesting. These places are located on the axes of the shaped part 1.5 mm (axis x, Se = 0.79) resp. 1.7 mm (axis z, Se = 0.86) under the surface. Under certain circumstances (lower temperatures, higher rolling speed and thus also greater strain rate, greater size of the initial austenitic grain) these equivalent strain values do not have to be sufficient to cause the DRX.

3 Fig. 4. shows the strain rate distribution on the upper surface of the rolled bar, longitudinal strain zone section and cross sections with 2 mm spacing during forming in the prefinishing mill. The pictures indicate the zone of maximum strain rate on the rolled bar surface is located at the area of the first contact of the rolled bar with the pass wall. As the strain increases the maximum moves on the rolled bar surface towards the sides and the intense strain zone reaches more to the centre. The zone of retarded strain caused by friction forces can be clearly seen. At the strain zone end the rolled bar surface layers display strain rate increase. The situation can be analyzed better using the graphs in Fig Fig. 2. Distribution of equivalent strain along the section - prefinishing stand Fig. 3. Distribution of equivalent strain along the section finishing stand Fig. 4. Distribution of strain rate along the section and on surface prefinishing stand The courses of equivalent strain and strain rate have been monitored in relation to the position 16 of the selected points (sensors) in the shaped part cross section. Their location scheme is provided in the Fig. 5. The sensors are designed in such manner so they would enable detail analysis of the monitored parameters in the dimension of the axis x [100], axis z [001], in the direction [101] and on the shaped partsurface.

4 For each of the mentioned directions we will get a graph of equivalent strain and strain rate dependence on rolling time for pre-rolling and the finisher. Fig. 6. depicts a situation in the direction of the x axis. We can see that the deformation accrual in the individual points corresponds to the standard s-curve, whereat the largest deformation is in the center of the shaped part and it drops in the direction towards the free edge. The courses of the strain rate are not dramatic and in all cases show one maximum (comment: the strain rate is the derivation of the equivalent strain and therefore shows certain variations as a result of the numerical Fig. 5. Distribution of sensors model inexactness). The more dramatic course of the monitored values can be seen in the direction [100] on the finisher, when the direction is the same as the course of the main strain. The points close to the center of the shaped part have a similar course as at the previous stand, however the situation changes towards the surface. The sensor situated on the surface (red) shows a dramatic increase of the equivalent strain at the beginning of the actual deformation zone, which is significantly longer than in the central parts of the shaped part. This dramatic increase of the equivalent strain is demonstrated by a local maximum in the strain rate curve, which is close to 750 s -1. The following maximums and minimums are the result of too coarse FE mesh on the roll (distance of their peeks calculated through the roll speed exactly corresponds to the size of the final elements on the rolls surfaces). Fig. 6. Time distribution of strain and strain rate on sensors in direction [100] Fig. 7. depicts the situation in the direction of the z axis. Here, the situation is opposite to the situation in the x axis direction. In the pre-finisher the direction is the same as the direction of the main strain, which is again demonstrated by the local maximum of the strain rate at the beginning of the deformation strip. However, the strain rate reaches the values of only 450 s -1. The same is also the variation of this curve caused by the coarse FE mesh on the rolls, however also here we can observe increased strain rate at the output from the deformation zone, up to the value of 140 s -1. These two peeks border the area of heavier deformation during rolling caused by internal friction forces. Compared to the previous flat rolling results we can say that during rolling in calibers the both maximum strain rate areas are less significant [5]. Fig. 8. depicts the situation in the direction [101]. In this direction we can observe a very homogenous course of the equivalent strain from the center to the surface. At the end of the rolling process the difference between the center and the surface is not grater than Se = 0.15.

5 Fig. 7. Time distribution of strain and strain rate on sensors in direction [001] Fig. 8. Time distribution of strain and strain rate on sensors in direction [101] Fig. 9. depicts the situation on the surface of the shaped part. Here we can clearly differentiate the points, which came into a contact with the roll from the points on a free surface. All points on the shaped part surface, which came into contact with the roll, show a significant strain rate maximum in ranges from 400 to 750 s -1. Fig. 9. Time distribution of strain and strain rate on sensors at surface The last useful result of shown using the sensors is the course of temperature during the entire double reduction process at the ASC finisher. We can observe temperature increase due to the deformation, in the center of each shaped part by c. 22 C adequate to the deformation work, at the surface the temperature accrual varies per the stand. With regard to the rolling speed cooling of the surface layer due to heat

6 absorption by the rolls is minimal and entirely shadowed by the deformation heat re-heating. The shaped parts cool down evenly between the stands, however by only c. 2 C. 3. DISCUSSION The simulation made using FEM confirmed the originally assumed considerable nonuniformity of distribution of basic strain parameters (equivalent strain, strain rate and temperature) during the process of bar rolling in oval circle roll pass design. It is a common phenomenon which cannot be eliminated by any modification of the roll pass design system. Great differences in the monitored parameters can lead to different courses of the softening processes. Let s analyze our particular example from this viewpoint. Can there be a static recrystallization (SRX) between the passages? Let s consider the temperature of 873 C, equivalent strain of 0.65, the starting grain size 50 µm, then, for this steel, we have the time for softening 50 % of the structure by SRX 45 s. The delay between processes at the ASC stand is only s. Thus the SRX can be considered only at temperatures over C. Thus, it is clear that the only mechanism for the required grain refining remains the DRX. The critical deformation for the DRX initiation per (1) with these particular values of the constants: A = , p = 0.17, and q = 0.3, varies around ε c = 0.7 to 0.8. The lowest value corresponds to the center of the shaped parts, the highest to the surface areas. The reason for higher values of the critical deformation at the surface is the lower temperature and higher strain rate [3]. Thus it is clear that during the first reduction the DRX does not occur (it would be necessary to for example increase the temperature to c. 910 C, however the DRX would not be possible in the entire volume, and thus it is not desirable in the first pass). Thanks to the cumulated strain the DRX occurs in during the second pass. In the areas of the minimum equivalent strain (see the Fig. 3.), the critical deformation is exceeded, but only by a minimum and in the event of temperature decrease by c. 30 C, or at the initial austenitic grain size increase from 50 to 100 µm, the DRX will not occur in these areas. The objective of this simulation was to determine representative mean values of the monitored thermomechanical values for the purposes of, for example, plastometric tests. Based on the achieved results it is clear that the predicting ability of these values would be very low. Thus, it would be useful to plastometrically review the central part of the shaped part separately to the areas under the surface on the x and z axes. This investigation was conducted with the support of Ministry of education, youth and sports of the Czech REFERENCES Republic under the research plan MSM [1] BIANCHI, J.H., KARJALAINEN, L.P. Modelling of Dynamic and Metadynamic Recrystallisation During Bar Rolling of a Medium Carbon Spring Steel. Journal of Materials Processing Technology, 2005, No. 160, p [2] LENARD,J.G., PIETRZYK, M., CSER, Y. Mathematical and Physical Simulation of the Properties of Hot Rolled Products. Elsevier Science Ltd., 1999, ISBN [3] FABÍK, R., et al. Verification of New Model for Calculation OF Critical Strain for the Initialization of Dynamic recrystallization Using laboratory rolling. Metalurgija Metallurgy, 2009, g. 48, br. 4, s ISSN (print), (online) [4] AKSENOV S., KLIBER J., CHUMACHENKO E. Comparison of 3D and 2.5D finite element simulation principles for rolling in grooves modeling. In Computer methods in materials science, Vol.7, 2007, p , ISSN [5] FABÍK, R., AKSENOV, S. Effect of Dynamic Changes of Thermomechanical Conditions During Hot Rolling of AISI304 Steel on Critical Strain for the Initiation of DRX. Hutnik wiadomości hutnice, 2008, roč. 76, č. 8, s ISSN