Segregation and Microstructure in Continuous Casting Shell

Transcription

1 Segregation and Microstructure in Continuous Casting Shell Brian G. Thomas and Young-Mok Won Department of Mechanical & Industrial Engineering University of Illinois at Urbana-Champaign September 25,

2 Objectives Develop a fast, simple microsegregation model for the solidification of multicomponent steel alloys. Implement model into other macroscopic models such as heat flow and thermal-stress analysis (CON1D and CON2D) and apply models to continuous casting. 2

3 Simple Microsegregation Model -based on the Clyne-Kurz model; -extended to account for multiple components, columnar dendrite microstructure, coarsening and /γ transformation. = 1 1 βk 1 C L C o (1 βk)/(k 1) where β = 2α + 1 exp 1 α + exp 1, 2α + α + = 2(α + α C ) and α C = 0.1 α = D S t f X 2 t f = T liq T sol C R 3

4 Assumption for Simple Model 1. Complete diffusion in the liquid phase. 2. Local equilibrium at the solid-liquid interface. 3. The equilibrium partition coefficient of solute elements applies at the solid-liquid interface and is constant throughout solidification. 4. Nucleation undercooling effects are negligible. 5. Fluid flow effects are negligible. 4

5 λ SDAS, µm Secondary Dendrite Arm Spacing Model λ SDAS (µm) = ( C C ) C R for C C 0.15 [1] [2] [1] Measured datas [2] = C R C C ( C) for C C > ~0.1 o C/sec ~0.2 ~0.5 ~2.0 ~5.0 ~1200 [2] [3] [2] Carbon Content, wt% 0.03 o C/sec [4] [5] C R = cooling rate ( o C/sec) C C = carbon content (wt%) References 1. H. Jacobi et al. : Steel Res., 1999, v70, p B. Weisgerber et al. : Steel Res., 1999, v70, p M. Imagumbai et al. : ISIJ Int., 1994, v34, p D. Senk et al. : Steel Res., 1999, v70, p A. Suzuki et al.: Nippon Kinzoku Gakkaishi, 1968, v32, p.1301.

6 Multicomponent Alloy Effect * Liquid temperature for a given liquid composition at the solidliquid interface T( o C) = %C 7.6 %Si 4.9 %Mn 34.4 %P 38 %S where %X (X = C, Si, Mn, P, S) is the liquid concentration at the solid-liquid interface. * Initial guess (equilibrium solidus temperature) => Solidus temperature, T sol, is given when = 1.0 6

7 Peritectic Phase Transformation Effect * Starting temperature of d/g transformation / T γ start ( o C) = T Ar4 = %C 60 %Si +12 %Mn 140 %P 160 %S where / %X (X = C,Si,Mn, P,S) = k L X C L,X * Ending temperature of d/g transformation C L,C 0.53wt%C * Solid fraction of d- and g-phase in the solid = / f γ end / f γ / γ end f start 2 * Average liquid concentration during the d/g transformation and γ = C ave L, i = C L, i + γ γ C L,i 7

8 Equilibrium Partition Coefficient and Diffusion Coefficient oolute Elements Element k d/l k g/l D d (cm 2 /sec) D g (cm 2 /sec) C exp(-19450/RT) exp(-32160/RT) Si exp(-59500/RT) 0.3exp(-60100/RT) Mn exp(-53640/RT) 0.055exp(-59600/RT) P exp(-55000/RT) 0.01exp(-43700/RT) S exp(-51300/RT) 2.4exp(-53400/RT) * R is gas constant in cal/mol and T is temperature in K. 8

9 1-D D Finite-Difference Model for Microsegregation local equilibrium domain A j L j 2 γ liquid 1 j = N = 100 d g L Solute diffusion calculation with FDM x j complete mixing * Diffusion equation and initial and boundary conditions for calculation. C S,i t = x D (T) C S,i S,i x C I. C. C S, i = k S / L S,i C o,i at t = 0 B.C. x = 0 at x = 0, λ / 2 SDAS 9

10 Validation (Case 1) Eutectic Fraction, % Solidification time, sec measured data[1] numerical prediction[2] simple model Cooling Rate, o C/sec Al-4.9%Cu alloy system C L = 33.2%Cu k = D S (cm 2 /sec) = λ SDAS (µm) =46.6 C R T liq ( o C) = C o References 1. Sareal et al. : Metall. Trans. B, 1986, v17a, pp Voller et al. : Metall. Tarns. A, 1999, v30a, pp

11 Validation (Case 2) 0.13%C-0.35%Si-1.52%Mn-0.016%P-0.002%S Mn in Liquid Phase, wt% C R = o C/sec Scheil Clyne-Kurz & Ohnaka(2α) Ohnaka(4α) simple model present FDM Brody-Flemings Lever rule C in Liquid Phase, wt% C R = 0.25 o C/sec Scheil Clyne-Kurz & Ohnaka(2α) Ohnaka(4α) & simple model present FDM Lever rule Brody-Flemings 1.8 α = k = 0.77 C o = Solid Fraction Solid Fraction α = k = 0.19 C o = 0.13

12 Validation (Case 3) 0.13%C-0.35%Si-1.52%Mn-0.016%P-0.002%S Mn in Liquid Phase, wt% cooling rate ( o C/sec) measured data[1] (360) (100) present FDM (assumed DAS) (360) (100) simple model (assumed DAS) (348) (149) simple model (SDAS in Eq.12) P in Liquid Phase, wt% cooling rate ( o C/sec) measured data[1] (360) (100) present FDM (assumed DAS) (360) (100) simple model (assumed DAS) (348) (149) simple model (SDAS in Eq.12) Solid Fraction Solid Fraction Reference 1. T. Matsumiya et al. : Trans. ISIJ, 1984, v24, pp

13 Validation (Case 4) Temperature, o C %Si-1.05%Mn %P %S C R = 0.17 o C/sec +γ γ +L +γ+l γ+l Liquid =0.0 =0.75 ZST(exp.)[1] ZDT(exp.)[1] 1350 Fe-C equilibrium diagram present FDM =1.0 simple model Carbon Content, wt% Temperature, o C %Si-1.52%Mn-0.012%P-0.015%S C R = 10.0 o C/sec +γ +L γ +γ+l γ+l Liquid =0.0 =0.75 ZST(exp.)[2] 1350 ZDT(exp.)[2] Fe-C equilibrium diagram present FDM simple model = Carbon Content, wt% Reference 1. G. Shin et al. : Tetsu-to-Hagane, 1992, v78, pp E. Schmidtmann et al. : Arch. Eisenhuttenwes., 1983, v54, pp

14 Validation (Case 5) Calculated Temperature, o C ZST (55 points) ZDT (53 points) Liquidus (48 points) /γ transformation (30 points) Solidus (47 points) Experimental Temperature, o C 1. Hot Tensile Tests - Zero Strength Temp.[1-4] - Zero Ductility Temp.[1-5] 2. Differential Thermal Analysis - Liquidus Temp.[6-9] - Solidus Temp.[6-9] - peritectic Temp. [6-8] References 1. G. Shin et al. : Tetsu-to-Hagane, 1992, v78, p D. J. Seol et al : ISIJ Int., 2000, v40, p E. Schmidtmann et al : Acrh. Eisenhuttenwe., 1983, v54, p T. Nakagawa et al. : ISIJ Int., v35, p H. G. Suzuki et al. : Trans. ISIJ, 1984, v24, p A Guide to the Solidification oteels, L. Ericson : Scand. J. Metall., 1977, v6, p S. Kobayashi : Trans. ISIJ, 1988, v28, p POSCO data. 14

15 Effects of C R and l SDAS on Segregation (by Simple Model) Effect of C R ( l SDAS = const.) Effect of l SDAS ( C R = const.) Phase Fraction constant λ SDAS, (µm) C R, ( o C/sec) γ L γ 0.18C (45.1) 0.8C (λ SDAS =79.0) L 0.044C (44.1) L Phase Fraction constant C R =10 o C/sec λ SDAS, (µm) 0.044C 0.18C 0.8C C L γ L γ L 0.18C 0.8C Temperature, o C Temperature, o C * Composition :0.044%C, 0.18%C, 0.8%C (-0.34%Si-1.52%Mn-0.012%P-0.015%S) 15

16 Combined Effects of C R and l SDAS on Segregation By Simple Model By Finite Difference Model C C Phase Fraction using λ SDAS in Eq. (12) C R, ( o C/sec) γ L L γ 0.18C 0.8C L Phase Fraction using λ SDAS in Eq. (12) C R, ( o C/sec) γ L L γ 0.18C 0.8C L Temperature, o C Temperature, o C * Composition :0.044%C, 0.18%C, 0.8%C (-0.34%Si-1.52%Mn-0.012%P-0.015%S) 16

17 Calculated Solidus Temperatures using Simple Model for Plain Carbon Steels 0.044wt%C 0.18wt%C 0.8wt%C C R λ SDAS T sol λ SDAS T sol λ SDAS T sol 1. Constant secondary dendrite arm spacing Constant cooling rate Combined effects of cooling rate and secondary dendrite arm spacing

18 Non-equilibrium Phase Diagram Calculated with Simple Model %Si-1.52%Mn-0.012%P-0.015%S Temperature, o C L γ cooling rate ( o C/sec) γ+l Carbon Content, wt% 18 γ+l Liquid =1.0 =0.0 =0.75 =0.9

19 Conclusions 1. A simple microsegregation model based on the Clyne-Kurz model developed. 2. A new equation for l SDAS proposed. l SDAS (mm) = ( C C ) C R for C C 0.15 = C R C ( C) C for C C > T sol is lowered significantly with independent increases in either C R or l SDAS. 4. The effect of C R less than 100 o C/sec on phase fraction evolution is insignificant in low alloy steels with less than 0.1wt%C, or for phase fractions below 0.9 in other steels 5. Phosphorus and sulfur have a significant effect on solidus temperature due to their enhanced segregation near the final stage of solidification. 6. The simple analytical model presented easily and efficiently incorporate microsegregation phenomena into solidification calculations for use in advanced macroscopic models. 19

20 Applications with CON1D * Conditions for Calculation - Steel compositions : %C-0.34%Si-1.52%Mn-0.012%P-0.015%S - Casting speed : m/min - Slab dimension : 960 mm * mm - Working mold length : 1096 mm - Superheat : 1 o C * Predicted T liq and T sol at strand surface using simple model (after iteration) C (wt%) t f (sec) C R ( o C/sec) l SDAS (mm) T liq ( o C) T sol ( o C)

21 Prediction of Phase Fraction (at 10 mm from surface) Solid Fraction Simple FDM 0.003C 0.044C 0.1C 0.18C 0.3C 0.44C 0.6C 0.8C Temperature, o C Phase Fraction Simple FDM 0.1C 0.18C 0.3C 0.44C γ L γ L L γ γ L Temperature, o C 21

22 Prediction of t f, C R and l SDAS Profiles Solidification Time, sec C 0.044C 0.1C 0.18C 0.3C 0.44C 0.6C 0.8C Average Cooling Rate, o C/sec C 0.044C 0.1C 0.18C 0.3C 0.44C 0.6C 0.8C Distance from Surface, mm Distance from Surface, mm 160 Seconary Dendrite Arm Spacing, µm C 0.044C 0.1C 0.18C Distance from Surface, mm 0.3C 0.44C 0.6C 0.8C

23 Predicted Effect of Carbon Content on T sol Variation through Shell Thickness at Mold Exit C C C T sol, o C o C T sol, o C o C T sol, o C o C T sol, o C C Distance from Surface, mm o C Distance from Surface, mm 1340 T sol, o C C T sol, o C o C Distance from Surface, mm C Distance from Surface, mm o C Distance from Surface, mm C T sol, o C T sol, o C o C Distance from Surface, mm C Distance from Surface, mm o C Distance from Surface, mm

24 Microsegregation Model Implemented into CON1D new outputs: t f, C R, l SDAS and T sol profiles Future Work (1) Maximum C L,i (composition between dendrites) and minimum C S,i (composition at dendrite trunks) (2) Non-equilibrium phase diagrams (3) Stainless steel (4) Macrosegregation 24