Simulation of Microstructural Evolution in Rod Rolling of a Medium C-Mn Steel. P. A. Manohar, Kyuhwan Lim, A. D. Rollett and Youngseog Lee *

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1 Simulation of Microstructural Evolution in Rod Rolling of a Medium C-Mn Steel P. A. Manohar, Kyuhwan Lim, A. D. Rollett and Youngseog Lee * Department of Materials Science and Engineering, Carnegie Mellon University, 5 Forbes Avenue, Pittsburgh, PA 15213, USA. manohar@andrew.cmu.edu; kyuhwal@andrew.cmu.edu; rollett@andrew.cmu.edu * Plate and Rod research group, POSCO Technical Research Laboratory, Pohang, P.O. Box 36, KOREA. pc554162@posco.co.kr Keywords: Rod Rolling, Microstructural Evolution, Mathematical Modelling, Process Optimization, Recrystallization Kinetics. Abstract. An Expert System is proposed in this work to conduct computational exploration of the deformation and restoration behavior of a medium C-Mn steel under high strain rate conditions, at elevated temperatures and complex strain paths that occur in rod rolling process. The expert system computes appropriate thermomechanical parameters necessary for describing rod rolling process in detail and then utilizes these parameters in mathematical models to determine microstructure evolution during a typical industrial-scale rod rolling process. Microstructure simulation in rod rolling is a challenging problem due to the fact that several softening mechanisms may operate sequentially or concurrently during each deformation step. Different softening mechanisms have very different impact on microstructure development and therefore it is important to investigate the particular combinations of processing conditions under which transition of operating softening mechanisms occurs. In the present work, the transition from dynamic to metadynamic recrystallization is studied in detail based on the criteria of critical strain, austenite grain size and Zener-Hollomon parameter when the interpass (interdeformation) time is very short of the order of few milliseconds during the later stages of rod rolling. Computational results are subsequently validated by comparing the program output to in-plant measured microstructure data. The proposed expert system is designed as an off-line simulation tool to examine and assess the various options for thermomechanical process optimization. Introduction Optimization of the industrial rod rolling process presents a formidable challenge as this process is characterized by continuous multi-pass deformation (up to 3 deformation passes) at high strain rate in the range.4 3s -1, at elevated temperatures in the range K, and very short interpass times of the order.15 1.s. These processing conditions make it virtually impossible to study experimentally the microstructural evolution during the intermediate stages of hot rolling. On the other hand, knowledge of the in-process microstructural evolution is important for both the optimization of the process schedule and to adjust the properties of the hot rolled product [1,2]. For example, a fine austenite grain size is desirable at the end of rod rolling to decreases its hardenability to obtain a fine ferrite + pearlite structure via controlled cooling, to eliminate or reduce the necessity of post-rolling annealing treatment, and to improve the mechanical properties of the as-rolled products. Previous efforts [3-5] to simulate microstructural evolution in wire rod rolling have concentrated mainly on calculating evolution of the mean austenite grain size in medium C-Mn steels. In the present work, the focus is on the fundamental aspects of microstructure development mechanisms such as static, dynamic and metadynamic recrystallization (SRX, DRX and MDRX respectively) and their kinetics, how to resolve the boundary conditions when they operate concurrently and finally their impact on microstructure evolution in continuous processing.

2 Expert System Development The flow chart for the expert system is given in Figure 1 located at the end of the text. The initial (i.e. as-reheated) microstructure and expected rolling schedule are the basic inputs to the system. The program then calculates the deformation conditions such critical and peak strains, and Zener Hollomon parameter based on initial grain size, pass strain, strain rate and temperature. The program subsequently computes the evolution of microstructure by computation of the recrystallized grain size, fraction recrystallized and recrystallization kinetics for a given rolling pass based on the mathematical models listed in Table 1. Table 1: Mathematical models describing kinetics of relevant softening mechanisms. Parameter DRX MDRX SRX Fraction Recrystallized k (F x ) [6-8] 1 exp(-.693 x 1 exp(-.693(t/t.5 )) ε ε 1 exp B c (t/t.5 ) 1.5 ) ε p B = -.8, K = 1.4, ε = 1.23 x ε c Time for 5% Recrystallization (t.5 ) [8-9] Recrystallized Grain Size (D rex ) [8-9] Finding D when partial [1] and / or combined [11] rex mechanisms operate Peak Strain (ε p ) [12] Pass Strain (ε) [8] Zener Hollomon Parameter (Z) [9] Austenite Grain Growth [4] p -.44 x ε& x 1-13 x ε -3.8 x ε& -.41 x exp(252/rt) 3.9 x 1 4 x Z x1 4 xz x D.67 o x ε -.67 Partial SRX: DRX + MDRX: D = F X DRX 4 / 3 D rex + ( 1 MDRX F X ) DRX 2 D D = D + ( D D ) xf o XMDRX 6.97 x 1 4 x D.3 o x - - Z.17 ε = ε pass + ε ε = K x ε previous x (1-F x ); K = 1 if F x <.1; K =.5 if F x.1 ε& x exp(3/rt) When time for grain growth is 1s: SRX: D f 7 D o 7 = 1.5 x1 27 x exp(-4/rt) x (t 4.32 x t.5 ) MDRX: D f 7 D o 7 = 8.2 x1 25 x exp(-4/rt) x (t 2.65 x t.5 ) When time for grain growth is < 1s: SRX: D f 2 D o 2 = 4. x1 7 x exp(-113/rt) x (t 4.32 x t.5 ) MDRX: D f 2 D o 2 = 1.2 x1 7 x exp(-113/rt) x (t 2.65 x t.5 ) Evolution of mean austenite grain size and the corresponding strain rate as a function of rolling pass is shown in Figure 2 overleaf. The austenite grain size is refined form an initial value of ~3 µm down to ~3.3 µm after finish rolling. Significant increases in mean austenite grain size due to in-process grain growth during the TMP delays are also evident in Fig. 2. This process is iterated until the rolling sequence is finished. The austenite grains coarsen to a mean size of ~15 µm during cooling from finish rolling temperature to the cooling stop temperature (CST), and subsequently during slower cooling form CST to Ar 3. This not surprising because the material studied is medium C-Mn steel where the grain growth is not inhibited by second phase particles or through any significant solute drag effect. Also, the grain growth rate is expected to be high as the grain size is very fine at this stage [13]. This means that

3 the advantage gained in refining the austenite grain size through DRX and MDRX during rolling is lost to an extent during the cooling segments. Strain Rate(s -1 ) Strain Rate γ Grain Diameter γ Grain Diameter(µm) Pass. Figure 2. Calculated mean γ grain size and average strain rate during rod rolling. Model Validation The specimens obtained from an industrial rod rolling mill at POSCO were sectioned, mounted, polished and etched in 4% Nital in the usual way. The micrographs were taken with a Philips SEM at 4X and 3X to obtain the appropriate resolution for austenite grain size and ferrite grain size respectively. Austenite microstructures are presented in Figure 3a and 3b while ferrite microstructures are presented in Figure 4a and 4b overleaf. The images taken for measuring austenite grain size were traced along ferrite grains precipitated along prior austenite grain boundary to delineate prior austenite grains. It should be mentioned here that some experience and judgment is necessary in tracing the prior austenite boundaries. The average austenite grain size was subsequently determined using the Scion-Image image analysis program to measure area of each grain on the traced image and equal area diameter was calculated according to the procedure outlined in the relevant ASTM standard [14]. The predicted austenite grain size just before the onset of γ α transformation is 15.2 µm while the measured prior austenite grain size in industrially processed steel is 14.4 µm. The transformed ferrite grain size is measured to be 4.6 µm while the predicted ferrite grain size is 4.9 µm. It is clear from this data that the predicted and experimentally measured mean austenite and ferrite grain size compare quite well, which validates the simulation procedure. Discussion Particular combinations of microstructural and processing conditions that lead to DRX and MDRX may now be analyzed in more detail based on the results of the expert system. In the current work, kinetics of dynamic recrystallization expressed in terms of peak and critical strain was utilized. The peak and critical strains were calculated based on the following relations [12]: ε p = 6.97 x 1 4 x D.3 o x Z.17 (1) ε c =.81 x ε p (2) Eq. (1) includes the effect of initial austenite grain size (controls diffusion path length), and temperature-compensated strain rate (Zener-Hollomon parameter) on strain accumulation and relaxation, which in turn decide the critical strain for the onset of DRX.

4 (a) (b) Figure 3. (a) SEM micrograph (3X) of industrially processed steel, and (b) prior γ grain boundaries are traced to determine austenite grain size just before γ α transformation. Measured mean γ grain size is 14.4 µm while model predicted it to be 15.2 µm. (a) (b) Figure 4. (a) SEM micrograph (4X) of industrially processed steel, and (b) Image processing to extract ferrite microstructure from the microstructure shown in (a). Measured mean α grain size is 4.9 µm while model calculation result was 4.6 µm. In the strain range from ε c and ε p, DRX will initiate, but perhaps will not lead to completion when the interpass times are short. In such cases, the amount of material recrystallized dynamically is computed according to a version of JMAK kinetics given according to the following equation [6]: k F XDRX = ε ε 1 exp B c (3) ε p Eqs. (1-3) then allow one to calculate exactly the relative amounts of dynamically and metadynamically recrystallized material during any deformation pass. Based on the foregoing analysis, the major operating mechanism as a function of austenite grain size and Zener-Hollomon parameter is determined for TMP sequence studied in this work as shown in Figure 5. The three-dimensional plot shown in Fig. 5 provides further insight in to particular combinations of process and microstructural variables for SRX, DRX and MDRX to occur. The points for MDRX in Fig. 5 are clustered, which indicates that MDRX is the dominant softening mechanism when the austenite grain size is relatively small (3 17 µm) and Zener-Hollomon parameter is in the range 5 7 x The DRX is dominant where the austenite grain size is in the range 2 4 µm and the Zener-Hollomon parameter is comparatively low in the range.2.5 x The SRX dominates when pass strain does not exceed the critical strain for a given pass, as expected.

5 Recrystallization Type Austenite Grain Size(µm) Z(X1 14 s -1 ) Figure 5: Operating recrystallization mechanism as a function of austenite grain size and Zener- Hollomon parameter. Key: Recrystallization Type 1 = 9% SRX; Type 2 = < 9% SRX (i.e. partial SRX) Type 3 = 9% MDRX Type 4 = < 9% MDRX (i.e. DRX+MDRX). Conclusions 1. An expert system is proposed in this work to compute the microstructural evolution in rod rolling that involves high strain rate deformation and complex strain paths. The predicted austenite microstructure at the end of rolling and the ferrite grain size subsequent to transformation correlate well with the data obtained from industrially processed material thus validating the simulation procedure. 2. Boundary conditions for DRX and MDRX have been resolved based on critical strain, austenite grain size and Zener-Hollomon parameter. It was found that MDRX dominates when austenite grain size is comparatively fine (3 17 µm) and Zener-Hollomon parameter is relatively high (5 7 x 1 14 ) compared to conditions for DRX (D o = 2 4 µm, Z =.2.5 x 1 14 ). References [1] S-H. Cho, K-B. Kang and J. J. Jonas J. J.: ISIJ Int., 41(21), p. 63. [2] H. F. Labib, Y. M. Youssef, R. J. Dashwood and P. D. Lee: Mater. Sci. Technol., 17(21), p [3] E. Anelli E. ISIJ Int., 32(1992), p. 44. [4] T. M. Maccagno, J. J. Jonas and P. D. Hodgson: ISIJ Int., 36(1996), p. 72. [5] A. Zufia and J. M. Llanos: ISIJ Int., 41(21), p [6] P. D. Hodgson: Ph. D. Thesis, (1993), University of Queensland, Australia. [7] P. D. Hodgson and R. K. Gibbs ISIJ Int., 32(1992), p [8] A. Laasraoui and J. J. Jonas: ISIJ Int., 31(1991), p. 95. [9] P. D. Hodgson: Proc. int. conf. Thermec 97, ed. by T. Chandra and T. Sakai, TMS, Wollongong, Australia, (1997), p.121. [1] J. M. Beynon and C. M. Sellars: ISIJ Int., 32(1992), p [11] J. G. Lenard, M. Pietrzyk and L. Cser: Mathematical and physical simulation of the properties of hot rolled products. Elsevier Science, UK, 1 st Ed., (1992), pp [12] C. M. Sellars: Mater. Sci. Technol., 6(199), p [13] M. Hillert: Acta metall., 13(1965), p [14] ASTM Standard E : Annual book of ASTM Standards, 3.1(22), pp

6 START Input composition, initial microstructure and rolling schedule Calculate ε c, ε p, Z ε > ε c? SRX Condition Calculate F XSRX, t.5 F XDRX 9? F XSRX 9? DRX + MDRX Calculate F x, t.5, D Full DRX Calculate F x, D rex Partial SRX Calculate D Full SRX Calculate D rex Calculate in-process grain growth Next Pass Rolling finished? Calculate non-isothermal grain growth Calculate Ferrite Grain Size END Figure 1: Flow chart for the expert system to determine microstructural evolution.