Segregation and Microstructure in Continuous Casting Shell

1University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Youngmok WON

Segregation and MicrostructureSegregation and Microstructurein Continuous Casting Shellin Continuous Casting Shell

Brian G. Thomas and Young-Mok Won

Department of Mechanical & Industrial EngineeringUniversity of Illinois at Urbana-Champaign

September 25, 2000


ObjectivesObjectives

•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.


Simple Microsegregation ModelSimple Microsegregation Model

-based on the Clyne-Kurz model; -extended to account for multiple components, columnar dendrite microstructure, coarsening and δ/γ transformation.

fS =1

1 −βk1−

CL

Co

(1−βk ) /(k −1)

β = 2α+ 1− exp −1

α+

− exp −

12α +

,

α+ = 2(α + αC) and αC = 0.1

α =DS t f

X2t f =

Tliq − Tsol

CR

where


Assumption for Simple Model 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 constantthroughout solidification.

4. Nucleation undercooling effects are negligible.

5. Fluid flow effects are negligible.


Secondary Dendrite Arm Spacing Model Secondary Dendrite Arm Spacing Model

λSDAS (µm) = (169.1-720.9 CC) CR-0.4835 for CC ≤ 0.15

= 143.9 CR-0.3616 CC

(0.5501-1.996C) for CC > 0.15

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

1000

[5]

[1]

[1]

[2]

[2]

[3]

[2][2]

[4]

0.1

0.2

0.5

2.05.0

0.03 oC/sec

Measured datas

0.03~0.1 oC/sec ~0.2 ~0.5 ~2.0 ~5.0 ~1200

λ SD

AS, µ

m

Carbon Content, wt%

References1. H. Jacobi et al. : Steel Res., 1999, v70, p. 357.2. B. Weisgerber et al. : Steel Res., 1999, v70,

p. 362.3. M. Imagumbai et al. : ISIJ Int., 1994, v34,

p.574.4. D. Senk et al. : Steel Res., 1999, v70, p. 368.5. A. Suzuki et al.: Nippon Kinzoku Gakkaishi,

1968, v32, p.1301.

CR = cooling rate (oC/sec)CC = carbon content (wt%)

* Liquid temperature for a given liquid composition at the solid-liquid interface

where %X (X = C, Si, Mn, P, S) is the liquid concentration at the solid-liquidinterface.

* Initial guess (equilibrium solidus temperature)

=> Solidus temperature, Tsol , is given when fS = 1.0


Multicomponent Multicomponent Alloy EffectAlloy Effect

T(oC) = 1536 − 78 ⋅%C − 7.6 ⋅ %Si − 4.9 ⋅%Mn − 34.4 ⋅%P − 38 ⋅%S


Peritectic Peritectic Phase Transformation EffectPhase Transformation Effect

Tstartδ / γ(oC) = TAr4 = 1392 +1122 ⋅ %C − 60 ⋅ %Si +12 ⋅%Mn −140 ⋅ %P −160 ⋅%S

where %X (X = C,Si,Mn, P,S) = kXδ / L ⋅ CL,X

δ

* Starting temperature of δ/γ transformation

* Ending temperature of δ/γ transformationCL,C ≥ 0.53wt%C

* Solid fraction of δ- and γ-phase in the solid

* Average liquid concentration during the δ/γ transformation

δ fS =fend

δ / γ − fS

fendδ / γ − fstart

δ / γ

2

⋅ fS and γ fS = fS−δ fS

CL, iave =

δ fS

fS

⋅CL, iδ +

γ fS

fS

⋅ CL,iγ


Equilibrium Partition Coefficient and DiffusionEquilibrium Partition Coefficient and DiffusionCoefficient of Solute ElementsCoefficient of Solute Elements

Element kδ/L kγ/L Dδ (cm2/sec) Dγ (cm2/sec)

C 0.19 0.34 0.0127exp(-19450/RT) 0.0761exp(-32160/RT)

Si 0.77 0.52 8.0exp(-59500/RT) 0.3exp(-60100/RT)

Mn 0.76 0.78 0.76exp(-53640/RT) 0.055exp(-59600/RT)

P 0.23 0.13 2.9exp(-55000/RT) 0.01exp(-43700/RT)

S 0.05 0.035 4.56exp(-51300/RT) 2.4exp(-53400/RT)

* R is gas constant in cal/mol and T is temperature in K.


11--D FiniteD Finite--Difference Model for MicrosegregationDifference Model for Microsegregation local equilibrium

complete mixing

Solute diffusion calculation with FDM

liquid δ γ

domain

2

Aj Lj

∆xj

L

δ

γ

1 j = N = 100

* Diffusion equation and initial and boundary conditions for calculation.

∂CS,i

∂t=

∂∂x

DS,i(T )∂CS,i

∂x

I. C. CS, i = kS / L ⋅ Co,i at t = 0 B.C.

∂CS,i

∂x= 0 at x = 0, λSDAS / 2


Validation Validation (Case 1)(Case 1)

0.01 0.1 1 10 100 10000

2

4

6

8

10

Solidification time, sec

measured data[1]

simple model

Eut

ectic

Fra

ctio

n, %

Cooling Rate, oC/sec

1000 100 10 1 0.1

numerical prediction[2]

Al-4.9%Cu alloy systemCL = 33.2%Cu

k = 0.145

DS (cm2/sec) = 5 × 10-9

λSDAS (µm) =46.6·CR-0.29

Tliq (oC) = 660-3.374 ·Co

References1. Sareal et al. : Metall. Trans. B, 1986, v17A,

pp. 2063-73.2. Voller et al. : Metall. Tarns. A, 1999, v30A,

pp. 2183-89.



0.5 0.6 0.7 0.8 0.9 1.01.5

1.8

2.1

2.4

2.7

3.0

α = 0.3738k = 0.77Co = 1.52

Scheil Clyne-Kurz & Ohnaka(2α) Ohnaka(4α) simple model present FDM Brody-Flemings Lever rule

Mn

in L

iqui

d P

hase

, wt%

Solid Fraction

0.5 0.6 0.7 0.8 0.9 1.00.0

0.2

0.4

0.6

0.8

1.0

α = 3.773k = 0.19Co = 0.13

Scheil Clyne-Kurz & Ohnaka(2α) Ohnaka(4α) & simple model present FDM Lever rule Brody-Flemings

C in

Liq

uid

Pha

se, w

t%

Solid Fraction

0.13%C-0.35%Si-1.52%Mn-0.016%P-0.002%S

CR = 0.045 oC/sec CR = 0.25 oC/sec



0.13%C-0.35%Si-1.52%Mn-0.016%P-0.002%S

0.0 0.2 0.4 0.6 0.8 1.01.4

1.6

1.8

2.0

2.2

2.4

0.045 0.25 cooling rate (oC/sec) measured data[1](360) (100) present FDM (assumed DAS)(360) (100) simple model (assumed DAS)(348) (149) simple model (SDAS in Eq.12)

Mn

in L

iqui

d P

hase

, wt%

Solid Fraction

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0.045 0.25 cooling rate (oC/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

Liq

uid

Pha

se, w

t%

Solid Fraction

Reference1. T. Matsumiya et al. : Trans. ISIJ, 1984, v24, pp. 873-82.



0.015%Si-1.05%Mn-0.0009%P-0.0008%SCR = 0.17 oC/sec

Reference1. G. Shin et al. : Tetsu-to-Hagane, 1992, v78, pp. 587-93.2. E. Schmidtmann et al. : Arch. Eisenhuttenwes., 1983, v54, pp. 357-62

0.0 0.2 0.4 0.6 0.8 1.01300

1350

1400

1450

1500

1550

ZST(exp.)[1] ZDT(exp.)[1] Fe-C equilibrium diagram present FDM simple model

δ

Liquid

δ+γ

δ+γ+L δ+L

γ+L

γ

fS=0.0

fS=0.75

fS=1.0

Tem

pera

ture

, o C

Carbon Content, wt%

0.0 0.2 0.4 0.6 0.8 1.01300

1350

1400

1450

1500

1550

Liquid

δ+γ

δ+γ+L

δ+L

γ+L

γ

δ

fS=0.0

fS=0.75

fS=1.0

ZST(exp.)[2] ZDT(exp.)[2] Fe-C equilibrium diagram present FDM simple model

Tem

pera

ture

, o C

Carbon Content, wt%

0.34%Si-1.52%Mn-0.012%P-0.015%SCR = 10.0 oC/sec



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]

References1. G. Shin et al. : Tetsu-to-Hagane, 1992, v78, p. 587..2. D. J. Seol et al : ISIJ Int., 2000, v40, p.356.3. E. Schmidtmann et al : Acrh. Eisenhuttenwe., 1983,

v54, p. 357.4. T. Nakagawa et al. : ISIJ Int., v35, p. 723.5. H. G. Suzuki et al. : Trans. ISIJ, 1984, v24, p. 54.6. A Guide to the Solidification of Steels, 1977.7. L. Ericson : Scand. J. Metall., 1977, v6, p. 116.8. S. Kobayashi : Trans. ISIJ, 1988, v28, p. 535.9. POSCO data.

1250 1300 1350 1400 1450 1500 15501250

1300

1350

1400

1450

1500

1550

ZST (55 points) ZDT (53 points) Liquidus (48 points) δ/γ transformation (30 points) Solidus (47 points)

Cal

cula

ted

Tem

pera

ture

, o C

Experimental Temperature, oC


Effects of CEffects of CRR and and λλSDASSDAS on Segregationon Segregation(by Simple Model)(by Simple Model)

1200 1250 1300 1350 1400 1450 1500 1550

0.0

0.2

0.4

0.6

0.8

1.00.044C (44.1)

0.18C(45.1)

0.8C(λSDAS=79.0)

L

L

L

γ

γ δ

δ

constant λSDAS, (µm)

CR, (oC/sec) 1 10 100

Pha

se F

ract

ion

Temperature, oC

1200 1250 1300 1350 1400 1450 1500 1550

0.0

0.2

0.4

0.6

0.8

1.0 0.044C

0.18C

0.8C

L

L

L

γ

γ δ

δ

constant CR=10 oC/sec λSDAS, (µm) 0.044C 0.18C 0.8C

137.4 103.7 182.0 44.1 45.1 79.0 14.2 19.6 34.4

Pha

se F

ract

ion

Temperature, oC

Effect of CR ( λSDAS = const.) Effect of λSDAS ( CR = const.)

* Composition :0.044%C, 0.18%C, 0.8%C (-0.34%Si-1.52%Mn-0.012%P-0.015%S)


Combined Effects of CCombined Effects of CRR and and λλSDASSDAS on Segregationon Segregation

By Simple Model By Finite Difference Model

1200 1250 1300 1350 1400 1450 1500 1550

0.0

0.2

0.4

0.6

0.8

1.0 0.044C

0.18C

0.8C

L

L

L

γ

γ δ

δ

using λSDAS in Eq. (12)

CR, (oC/sec) 1 10 100

Pha

se F

ract

ion

Temperature, oC

1200 1250 1300 1350 1400 1450 1500 1550

0.0

0.2

0.4

0.6

0.8

1.0 0.044C

0.18C

0.8C

LL

L

γ

γ δ

δ

using λSDAS in Eq. (12)

CR, (oC/sec) 1 10 100

Pha

se F

ract

ion

Temperature, oC

* Composition :0.044%C, 0.18%C, 0.8%C (-0.34%Si-1.52%Mn-0.012%P-0.015%S)


Calculated Solidus Temperatures Calculated Solidus Temperatures using Simple Model for Plain Carbon Steelsusing Simple Model for Plain Carbon Steels

0.044wt%C 0.18wt%C 0.8wt%C

CR λSDAS Tsol λSDAS Tsol λSDAS Tsol

1. Constant secondary dendrite arm spacing

1 44.1 1491.00 45.1 1455.64 79.0 1308.44

10 44.1 1487.86 45.1 1447.13 79.0 1287.40

100 44.1 1478.39 45.1 1428.13 79.0 1234.14

2. Constant cooling rate

10 137.4 1478.55 130.7 1434.06 182.0 1254.72

10 44.1 1487.86 45.1 1447.13 79.0 1287.40

10 14.2 1490.99 19.6 1454.00 34.4 1304.75

3. Combined effects of cooling rate and secondary dendrite arm spacing

1 137.4 1487.93 130.7 1450.38 182.0 1295.43

10 44.1 1487.86 45.1 1447.13 79.0 1287.40

100 14.2 1487.78 19.6 1442.83 34.4 1277.52


NonNon--equilibrium Phase Diagramequilibrium Phase DiagramCalculated with Simple ModelCalculated with Simple Model

0.34%Si-1.52%Mn-0.012%P-0.015%S

0.0 0.2 0.4 0.6 0.8

1300

1350

1400

1450

1500

1550

δ+L δ+γ+L

γ

δ γ+L

Liquid

fS=0.0

fS=0.75

fS=0.9

fS=1.0

cooling rate (oC/sec) 1 10 100

Tem

pera

ture

, o C

Carbon Content, wt%


ConclusionsConclusions

1. A simple microsegregation model based on the Clyne-Kurz model developed.

2. A new equation for λSDAS proposed.λSDAS (µm) = (169.1-720.9 CC) CR

-0.4835 for CC ≤ 0.15 = 143.9 CR

-0.3616 CC(0.5501-1.996C) for CC > 0.15

3. Tsol is lowered significantly with independent increases in either CR or λSDAS.

4. The effect of CR less than 100 oC/sec on phase fraction evolution is insignificantin 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 totheir enhanced segregation near the final stage of solidification.

6. The simple analytical model presented easily and efficiently incorporate micro-segregation phenomena into solidification calculations for use in advanced macroscopic models.


Applications with CON1D

* Conditions for Calculation- Steel compositions : %C-0.34%Si-1.52%Mn-0.012%P-0.015%S- Casting speed : 1.524 m/min- Slab dimension : 960 mm * 132.1 mm- Working mold length : 1096 mm- Superheat : 1 oC

* Predicted Tliq and Tsol at strand surface using simple model (after iteration)C (wt%) 0.003 0.044 0.1 0.18 0.3 0.44 0.6 0.8tf (sec) 0.303 0.350 0.437 0.575 0.846 1.268 1.862 2.862

CR (oC/sec) 73.5 96.6 114.1 120.5 113.0 97.8 82.5 65.1λSDAS (µm) 20.0 14.4 9.36 18.3 27.6 35.9 40.6 40.2

Tliq (oC) 1524.8 1521.6 1517.2 1511.0 1501.6 1490.7 1478.2 1462.6Tsol (oC) 1502.5 1487.7 1467.3 1441.7 1406.0 1366.7 1324.5 1276.4


1250 1300 1350 1400 1450 1500 1550

0.0

0.2

0.4

0.6

0.8

1.0

Simple FDM 0.003C 0.044C 0.1C 0.18C 0.3C 0.44C 0.6C 0.8C

Sol

id F

ract

ion

Temperature, oC

Prediction of Phase FractionPrediction of Phase Fraction(at 10 mm from surface)(at 10 mm from surface)

1375 1400 1425 1450 1475 1500 1525

0.0

0.2

0.4

0.6

0.8

1.0

L

L

L

γ

γ

γ L

γδ

δ

δ

δ

Simple FDM 0.1C 0.18C 0.3C 0.44C

Pha

se F

ract

ion

Temperature, oC


0 4 8 12 16 200

10

20

30

40

0.3C 0.44C 0.6C 0.8C

0.003C 0.044C 0.1C 0.18C

Sol

idifi

catio

n T

ime,

sec

Distance from Surface, mm

0 5 10 15 201

10

100

0.3C 0.44C 0.6C 0.8C

0.003C 0.044C 0.1C 0.18C

Ave

rage

Coo

ling

Rat

e, o C

/sec


Prediction of Prediction of ttff , C, CR R and and λλSDAS SDAS ProfilesProfiles

0 5 10 15 200

20

40

60

80

100

120

140

160

0.3C 0.44C 0.6C 0.8C

0.003C 0.044C 0.1C 0.18CS

econ

ary

Den

drite

Arm

Spa

cing

, µm



0 5 10 15 201502.3

1502.4

1502.5

1502.6

1502.7

0.003C

0.18oC

Tso

l, o C


0 5 10 15 201440

1442

1444

1446

1448

1450

0.18C

7.354oC

T sol,

o C


0 5 10 15 20

1276

1280

1284

1288 0.8C

11.361oC

T so

l, o C

Distance from Surface, mm0 5 10 15 20

1320

1325

1330

1335

1340

0.6C

11.622oC

T sol,

o C


0 5 10 15 201364

1368

1372

1376

1380

0.44C

11.097oC

T sol,

o C


1404

1408

1412

1416 0.3C

9.783oC

T sol,

o C


0 5 10 15 201467.2

1467.3

1467.4

1467.5

0.1C

0.132oC

Tso

l, o C


1487.6

1487.7

1487.8

1487.9

0.044C

0.139oC

Tso

l, o C


Predicted Effect of Carbon Content on Tsol Variationthrough Shell Thickness at Mold Exit


Microsegregation Model Implemented into CON1DMicrosegregation Model Implemented into CON1D

new outputs: tf , CR , λSDAS and Tsol profiles

Future WorkFuture Work(1) Maximum CL,i (composition between dendrites)

and minimum CS,i (composition at dendrite trunks)

(2) Non-equilibrium phase diagrams

(3) Stainless steel

(4) Macrosegregation

Documents

Segregation and Microstructure in Continuous Casting Shell