Numerical Analysis for the Prediction of Microstructure after Hot Forming of Structural Metals

Transcription

1 Materials Transactions, Vol. 50, No. 7 (2009) pp to 1625 Special Issue on New Functions and Properties of Engineering Materials Created by Designing and Processing #2009 The Japan Institute of Metals OVERVIEW Numerical Analysis for the Prediction of Microstructure after Hot Forming of Structural Metals Jun Yanagimoto* Institute of Industrial Science, The University of Tokyo, Tokyo , Japan The importance of structural metals for industrial applications is based on their superior combination of mechanical properties strength, elongation, toughness and corrosion resistance achieved at the end of forming processes. A numerical for the prediction of microstructure is strongly required for the optimization of hot forming process parameters, because the microstructure of structural metals, which has the significant effects on mechanical properties, is strongly dependent to forming process conditions as well as the chemical composition. The incremental dislocation density and microstructural evolution method enables the prediction of the change in microstructure after forming. The outline of the analytical scheme is explained briefly, and the results of its application to strip rolling, bar rolling and shape rolling are presented. Finally, the remaining research topics in this field are discussed. [doi: /matertrans.mf200906] (Received December 25, 2008; Accepted February 5, 2009; Published June 25, 2009) Keywords: forming, microstructure, analytical method, finite element method (FEM) 1. Introduction The most important demand for structural metals is that for good mechanical properties such as high strength, elongation, toughness and corrosion resistance. These properties are governed by the microstructure of formed product. Thus, the optimization of the forming conditions, or forming process parameters, referring to the microstructure of the formed product for the target values, is gaining increasing importance in the research and development of hot forming technologies. The above optimization of forming condition has two aspects of hardware and software technologies. The first one, hardware technologies, such as controlled rolling process, high reduction rolling mill, controlled and rapid cooling system and coiling system, has marked significant progress in the past decades, as has been reviewed by Ouchi. 1) The recent tandem hot strip rolling processes developed by Eto, Fukushima, Sasaki and co-workers 2) enable us to roll a strip of fine grained steel without the need to add any micro-alloying element such as niobium and vanadium. The major achievement of the software technologies is micro-alloying technologies used to control the change of the microstructure of hot metal being formed, as was reviewed by Ouchi 1) and Tamura. 3) The hardware and software technologies should be considered together, even though their individual optimal orientations within industrial applications are mutually opposing. This necessitates the numerical for predicting the microstructure of structural metal after hot forming in order to satisfy both requirements. In the following chapters, first, the outline and availability of the analytical scheme is explained. Here, the basic scheme of the incremental dislocation density and microstructural evolution is briefly explained. Then, the results of its application to strip rolling, bar rolling and shape rolling, which were obtained by the author, will be presented to show the effectiveness of the analytical method of the microstructural evolution and plastic deformation in the optimization of the forming process. *Corresponding author, yan@iis.u-tokyo.ac.jp 2. Analytical Method of Microstructural Evolution and Plastic Deformation in Hot Forming The analytical method of microstructural evolution is categorized into two groups. The first is the microstructure scheme. It contains the evolutional equation for the of grain structure, which is governed by metallurgical phenomena, such as work hardening, recovery and recrystallization of the material, caused by the transient change in the temperature and the strain rate of every material point. This scheme involves the use of the kinetics of microstructural evolution, which is called the material genome, as the boundary conditions in the. The analytical scheme used as the evolutional equation and the kinetics used as the material genome were not always distinguished in the past. The second group is the deformation scheme such as the finite element method. 2.1 Analytical scheme for the microstructure evolution Sellers and Whiteman 4) and Laasraoui and Jonas 5) carried out consistent investigations on microstructural evolution during the hot forming of steels, and the results of the experiments have been summarized as empirical models. Those empirical models have been used for the prediction of the industrial hot rolling process by Beynon and Sellers. 6) In their, the analytical scheme used as the evolutional equation and the kinetics used as the material genome were not always distinguished, so that the transient change in temperature and strain rate cannot be reflected in the microstructural change. This is almost the same as other microstructure methods proposed in 1970s and 1980s. Senuma and Yada 7,8) extensively investigated the measurement of the microstructural evolution of C-Si-Mn steels during hot compression, and they found equations on the kinetics of, for example, work hardening, dynamic and static recoveries, dynamic and static recrystallization and grain growth as functions of process variables such as temperature, strain rate and strain. 8) They proposed an analytical model to predict the flow stress and microstructural evolution, taking dislocation density as a representative variable. 9) They also

2 Numerical Analysis for the Prediction of Microstructure after Hot Forming of Structural Metals 1621 tried to express their model by the differential description aimed at estimating the microstructural evolution and flow stress after transient changes in process variables such as temperature and strain rate. However, their effort was not a total success, because of the insufficiency of numerical solution of their differential form. 10) Finite element of the metal forming process propagated in the 1980s after the pace-setting investigations on microstructural evolution in the hot forming of structural metals by Sellars et al., 4,6) Laasraoui and Jonas, 5) Senuma and Yada 7 10) and other researchers. As finite element can reveal the transient changes in temperature and strain rate at each point of the structural metal during forming, we need a new approach to reflect this transient change in process variables in the evolution of microstructure. This movement promoted the development of an evolutional method by Karhausen and Kopp 11) and an incremental dislocation density and microstructural evolution method by Yanagimoto et al. for dynamic events, 12) static events 13) and phase transformation. 14) The change in the dislocation density due to work hardening and dynamic recovery is expressed by the following eq. (1), as proposed by Senuma et al. 10) d ¼ cd" bdt ð1þ is an average dislocation density of grains. Because in eq. (1) is that for unrecrystallized grains, it is expressed as 0 with the superscript showing the number of recrystallization cycles. V 0, which is the volume fraction of the unrecrystallized structure, decreases with the progress of dynamic recrystallization, as expressed by V 0 ðt þ tþ ¼V 0 ðtþ X 0!1 : ð2þ X 0!1 is the recrystallized fraction within time interval t. In the same manner, the volume fraction of grains which underwent i-th cycle of dynamic recrystallization at time t þ t, V i ðt þ tþ, can be expressed as V i ðt þ tþ ¼V i ðtþ X i!iþ1 þ X i 1!i : ð3þ Here, X i!iþ1 shows the fraction recrystallized from V i within time interval t. The value of X i!iþ1 is expressed as X i!iþ1 ¼ V i ðtþ i ðtþx i!iþ1 ; ð4þ where x i!iþ1 is the relative recrystallized volume fraction and i ðtþ is the ratio of volume of grains in V i ðtþ, strain of which exceeds the critical strain for the onset of the next cycle of recrystallization to volume V i ðtþ. i ðtþ and x i!iþ1 can be derived from the equation for the progress of dynamic recrystallization from the unrecrystallized grains. 12) Thus, the average dislocation density and grain size of V i ðt þ tþ are respectively updated incrementally by i 1 ðt þ tþ ¼ V i ðt þ tþ fvi ðtþð i ðtþþ i Þ þ X i 1!i D g ð5þ d i 1 ðt þ tþ ¼ V i ðt þ tþ fvi ðt þ tþðd i ðtþþd i Þ þ X i 1!i d D g: ð6þ d i ðtþ is the average grain size of austenite grains that underwent the i-th cycle of recrystallization at time t. D and d D are the dislocation density and grain size of dynamically recrystallized grains, respectively. The value of D equals to the dislocation density of annealed grains. A similar scheme could be applied to the of the microstructure and dislocation density after static recrystallization. 13) The incremental dislocation density and microstructural evolution method is also applicable to phase transformation 14) based on conventional nucleation and grain growth theory. 9,15) The increment in the ferrite volume fraction, X, can be expressed by eqs. (7) and (8) for the nucleation stage and the site saturation stage. X ðtþ ¼4 1=4 ðiðtþs v1þ 1=4 ðg ðtþþ 3= =4 ln ð1 X ðt tþþt ð7þ 1 X ðt tþ X ðtþ ¼K 1 S v2 G ðtþð1 X ðt tþþt ð8þ Here, IðtÞ is the rate of nucleation, G ðtþ is the grain growth rate and K 1 is the material constant. S v1 and S v2 are the effective grain boundary area for nucleation stage and grain growth stage, respectively. The rate of nucleation IðtÞ is affected by the residual dislocation density of grains,, due to prior deformation, as expressed by eq. (9). The left-hand side of eq. (9), I 0 ðtþ, is substituted into eq. (7) in place of IðtÞ. The ferrite grain size, d, is expressed by eq. (10). I 0 ðtþ ¼ IðtÞ ð9þ D ( d ¼ 1: :75 0:25 d exp ) 1=3 X D ð10þ T 0:05 Here, T 0:05 is the temperature at 5% transformation and is a representative parameter of cooling rate. Numerical using eqs. (1) (10) with transient changes in the strain rate and temperature along stream line, that is the path of every material point at cross-section of metal subjected to plastic deformation during rolling, give us the results on microstructure and dislocation density of metal under hot forming. 2.2 Deformation Metal forming has two major functions: the first is the generation of product geometry, and the second is the generation of mechanical properties. The generation of product geometry is realized by designing the die profile and forming conditions for the material to be formed, and the deformation of the material being formed is of primary importance. From the beginning of the 20th century, the elementary and other analyses for the stress field of the material being formed had been developed and applied to reveal the deformation characteristics and to design the forming conditions. Such analyses can be represented by the two-dimensional rolling theory proposed by Karman 16) and Orowan. 17) In the last decade of the 20th century, finite element analyses of metal forming processes began to be used in practice ) An example of the shape rolling processes was presented by Yanagimoto et al. 21) and is illustrated in Fig. 1. The finite element simulation system built on computer cided design (CAD) platform is used as

3 1622 J. Yanagimoto Profile of caliber Nodal points for FE Angle Channel Asym. Sec. Asym. Sec. Fig. 1 CAE system for three-dimensional deformation of shape rolling built on CAD platform. the virtual rolling mill to replace the model experiment using lead or plasticine with digital data on a personal computer. The computer aided engineering (CAE) system for the metal forming process is now widely used in metal forming industries. With this system, the three-dimensional distribution of strain rate and temperature can be analyzed, and their transient change can be known, even that inside the material. Then, the challenging target for these CAE systems is to simulate the evolution of the microstructure of the metal, because the microstructure generated during hot forming has significant effects on the mechanical properties of the product. 2.3 Microstructure during hot forming induced by hot deformation The general construction of the analytical scheme is illustrated in Fig. 2, taking the hot strip rolling of a steel sheet as an example. A sketch of the microstructural evolution is also shown in this figure. The whole analytical scheme for the of the microstructural evolution is divided into several components: initial microstructure model, hot forming model, transformation model and microstructure-property model. The microstructure-property model is still the focus of many basic investigations, but no general approach is available. The hot forming model and transformation model are coupled with the three-dimensional finite element of various rolling processes. Figures 3 and Table 1 show the results of applying microstructural to the strip rolling process to elucidate the effect of the thickness reduction balance of the finishing train of hot strip mill on the final microstructure after transformation, as obtained by Morimoto et al. 22) Large thickness reductions at latter stands in the finishing train yield steel strips with finer grains. The analytical results agree well with the experimental measurements. Here, the incremental dislocation density and microstructural evolution method are used to estimate the dislocation density and microstructure in forming, 12) interpass 13) and transformation. 14) Figure 4 shows examples for bar rolling. 23) Here, the effect of the rolling mill type on the austenite grain distribution during rolling is clearly shown. Also, the cross-sectional distribution of final microstructure after cooling is successfully simulated. Figure 6 shows the examples of the shape rolling illustrated in Fig. 5. The cooling condition between and after stands has a significant effect on the cross-sectional distribution of microstructure after rolling. 24) 3. Current Situation and Remaining Issue As is presented in the following chapter, several results were obtained through the coupled of plastic deformation and microstructure. The general scheme of such coupled is shown in the Fig. 2. First of all, the microstructure-property model, which is not yet realized, is shown in Fig. 2. There are empirical equations presented and summarized by Pickering, 25) but we did not know the general method at present, even though extensive researches has long been carried out in this field by Esaka et al. 26) and

4 Numerical Analysis for the Prediction of Microstructure after Hot Forming of Structural Metals 1623 Furnace Roughening Finishing Cooling Coiling Initial microstructure model Hot forming model Transformation model Microstructure properties model Inverse transformation Grain growth Initial γ grain size γ grain size distr. Dislocation density distr. Incremental microstructural evolution and dislocation density method Hot deformation by FEM Temperature α grain size distr. Volume of each phase Phase field method Temperature Incremental transformation FEM for Tensile test Homogenization method F D Avrami s equation for DRX DRX grain size Material genome for an alloy σ Y B 0 N and GG rate G Grain growth rate N and G of precipitates Work hardening coeff. Recovery coeff. Precipitation model SRX grain size Avrami s equation for SRX Ferrite grain size SS curve of each phase Fig. 2 Integrated model for the evolution of microstructure in hot forming. Schedule A (conventional): Higher reductions in earlier stand in FT Schedule B (new): High reductions in latter stands in finishing trains Ferrite grain size d α / µm Measured grain size for schedule A Schedule A Schedule B Predicted grain size Measured grain size for schedule B Time on run-out table after final stand T ROT / s Volume fraction of each phase Predicted value Measured value Time on run-out table after final stand T ROT / s Fig. 3 Ferrite grain size and volume fraction of each phase after rolling. Tomota et al., 27) for example. Many more investigations are necessary to clarify the relationship between the microstructure and mechanical properties of the structural metals used in current society. Secondly, the material genome, that is, the empirical equation to describe, for example, work hardening, recovery and recrystallization as functions of strain rate, strain and temperature for each alloy composition, are missing in most of the structural steels. An example of material genome obtained by Senuma and Yada 7) is summarized in Fig. 7. As was explained earlier, deformation to obtain the transient change in strain rate and temperature for the material being formed is in practical use in several rolling processes. A microstructure method, such as the incremental dislocation density and microstructure evolution method, is proposed and applied to estimate the microstructure affected by the transient change in strain rate and temperature, using the material genome as the boundary condition. Then, we lack the material genome to describe, for example, work hardening, recovery and recrystallization as functions of strain rate, strain and temperature for each alloy composition. As numerous commercial structural metals are used, we require a huge number of experiments to obtain the material genome. This aspect is common to the first problem, which is the lack of a general model to connect the microstructure and mechanical properties. Then, it can be emphasized that

5 1624 J. Yanagimoto Table 1 Rolling conditions for strip rolling. Rolling condition Finisher entry temperature Ti/ C Finisher exit temperature Te/ C Coiling temperature Tc/ C Finisher inletting speed Vi /mms 1 Schedule A New schedule B Rolling Bar Thickness of rolled strip and reduction in each stand condition thickness F1 F2 F3 F4 F5 F6 Schedule A Schedule B 30.4 mm 40.2 mm 15.6 mm 8.7 mm 5.5 mm 3.5 mm 2.5 mm 2.0 mm 48% 44% 37% 36% 29% 20% 24.8 mm 15.6 mm 1 mm 6.3 mm 3.7 mm 2.3 mm 38% 37% 33% 40% 41% 38% Three-roll mill Two-roll mill ( µ m) Fig. 4 Austenite grain size distribution in rolled bar. Area reduction is 52% after four forming passes, and initial grain size is 80 mm. R1 R2 R3 U1 E1 U2 U3 E2 U4 U5 E3 IMC device UF TMCP device Distribution of austenite grain size µ m H R 20m 20m 40m 5m H F 30m 50m H F H W H W 8 Fig. 5 Mill layout and cooling system of H-beam rolling. (a) Air cooling between and after rolling (b) Water cooling between and after rolling µ m Distribution of ferrite grain size 20 innovative numerical methods of describing (1) the microstructure-mechanical property relationship, and (2) the kinetics of the change in microstructure as functions of strain rate and temperature, will be strongly required in the near future. These methods should enable the prediction of the above values for the complicated and diversified composition of microstructures, which are dependent on the chemical composition of the numerous commercial alloys. 4. Conclusion The numerical of microstructure after the hot forming of structural metals was explained in this paper. (a) Air cooling between and after rolling (b) Water cooling between and after rolling Fig. 6 Microstructures after H-beam rolling under different cooling conditions. Because of the difficulties and complexity of the numerical scheme, the practical application of this kind of consistent model to industrial processes is not always promoted, as was discussed by Bariani and co-workers, 28) particularly by

6 Numerical Analysis for the Prediction of Microstructure after Hot Forming of Structural Metals 1625 Deformation and temperature T n, ε n at every time step Microstructure as incremental dislocation density and microstructural evolution Distribution of grain size Distribution of dislocation density Flow stress σ = ρ Metallurgical model by Senuma (material genome) Work hardening coeff c = d0 Rate of dyn. recovery 8000 b = 9850 ε exp D R X Critical strain Rate of recrystr. DRX grain size Activation energy ε c 8000 = exp G D =, ε = d 0 ε exp 2 ε T d D = Z 0.27 Q = 266 [KJ/mol] Rate of static recovery b S = 63.0t S R X S γ d = exp 0.6 ( Sv ε) 8000 G = S, t = S Rate of recrystr. 2 v ε ε exp 2 t SRX grain size GB area γ S v 24 = (0.491exp π d 0 ( ε) exp( ε ) exp( 3ε ) Hot compression test at constant rate and temperature (measurement of flow stress and microstructure) Rate of grain growth α = Fig. 7 Example of material genome for plain carbon steel. forming scientists and engineers. More sophisticated software, built on the CAD platform, for predicting the microstructure and macroscopic deformation in industrial hot forming processes should be realized. There are two major drawbacks that must be solved: the lack of the material genome, or functions for the kinetics of recovery and recrystallization, and the microstructure-mechanical properties relationships for an alloy being formed. Extensive investigations on these topics are expected, probably using the numerical approach. Resolving these issues will open a new era of manufacturing science, where the simultaneous design and optimization to produce products with high performance will be realized for all structural metal used in social activities. REFERENCES 1) C. Ouchi: ISIJ Int. 41 (2001) ) M. Eto, S. Fukushima, T. Sasaki, Y. Haraguchi, K. Miyata, M. Wakita, T. Tomida, N. Imai, M. Yoshida and Y. Okada: ISIJ Int. 48 (2008) ) I. Tamura: Trans. ISIJ 27 (1987) ) C. M. Sellars and J. A. Whiteman: Metal Sci. 13 (1979) ) A. Laasraoui and J. J. Jonas: ISIJ Int. 31 (1991) ) J. H. Beynon and C. M. Sellars: ISIJ Int. 32 (1992) ) H. Yada, N. Matsuzu, K. Nakajima, K. Watanabe and H. Tokita: Trans. ISIJ 23 (1983) ) T. Senuma, H. Yada, Y. Matsumura and T. Futamura: Tetsu-to-Hagane 70 (1984) ) T. Senuma, M. Suehiro and H. Yada: ISIJ Int. 32 (1992) ) T. Senuma, H. Yada, Y. Matsumura, S. Hamauzu and K. Nakajima: Tetsu-to-Hagane 70 (1984) ) K. Karhausen and R. Kopp: Steel Research 63 (1992) ) J. Yanagimoto, K. Karhausen, A. J. Brand and R. Kopp: Trans. ASME, J. Manufact. Sci. Eng., 120 (1998) ) J. Yanagimoto and J. S. Liu: ISIJ Int. 39 (1999) ) J. S. Liu and J. Yanagimoto: ISIJ Int. 41 (2001) ) M. Suehiro, K. Sato, Y. Tsukao, H. Yada, T. Senuma and Y. Matsumura: Trans. ISIJ 27 (1987) ) T. Karman: Zeitschrift für Angewandte Mathematik und Mechanik 5 (1925) ) E. Orowan: Proc. Inst. Mech. Eng. 150 (1943) ) K. Mori and K. Osakada: Int. J. Mech. Sci. 24 (1982) ) K. Mori, K. Osakada and T. Oda: Int. J. Mech. Sci. 26 (1984) ) Y. Sodani, T. Hirakawa, K. Ikui, M. Hatanaka and K. Mori: Tetsu-to- Hagane 79 (1993) ) J. Yanagimoto, Y. Kadomura, T. Muto and K. Inoue: Steel Research 73 (2002) ) T. Morimoto, I. Chikushi and J. Yanagimoto: ISIJ Int. 47 (2007) ) J. Yanagimoto, T. Ito and J. S. Liu: ISIJ Int. 40 (2000) ) J. S. Liu and J. Yanagimoto: ISIJ Int. 42 (2002) ) F. B. Pickering: Physical Metallurgy and the Design of Steels (Elsevier 1978). 26) K. Esaka, J. Wakita, M. Takahashi, O. Kono and S. Harada: Seitetsu- Kenkyu 321 (1986) ) Y. Tomota, K. Kuroki, T. Mori and I. Tamura: Mater. Sci. Eng. 24 (1976) ) P. F. Bariani, T. Dal Negro and S. Bruschi S: CIRP Annals 53 (2004)