uiuc, august 5, 2009 thermal-mechanical behavior of the

ANNUAL REPORT 2009ANNUAL REPORT 2009UIUC, August 5, 2009

Thermal-mechanical Behavior ofthe Solidifying Shell Ideal Taperthe Solidifying Shell, Ideal Taper,

and Longitudinal Crack Formation

Lance C. Hibbeler

in a Funnel Mold Lance C. Hibbeler

(MSME/Ph.D. Student)

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign

Continuous Slab Casting Molds

Conventional Slab Casting Mold

Submerged Entry Nozzle (SEN)

Funnel Region

Casting Mold

M ld Wid

Mold Narrow Face (NF)

Mold Wide Face (WF)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 2

( )Solidifying Steel

Strand Thin-Slab Casting Funnel Mold

Funnel Mold Terminology and Nominal DimensionsNominal Dimensions

Strand Width = 1200 mm (47.2”) (Variable)Centerline Slice

Mold Wide Face

Funnel Crown = 23.4 mm (0.92”) top, 8 mm (0.32”) bottom

Funnel L

Mold

Outer Funnel Width = 750 mm (29.4”)

Inner Funnel Width = 260 mm (10.2”)Mold Narrow Face Mold Narrow Face

ength = 850

d Length = 11 m

m (33.5”)

100 mm

(43.3

Strand Thickness = 90 mm . (3.5”)

Funnel Opening = 136.8 mm (5.4”)

Outer InnerOuter Inner Inner Outer Outer

Mold Wide Face

3”)


OuterFlat

InnerCurve

OuterCurve

InnerFlat

InnerCurve

OuterCurve

OuterFlat 72 mm (2.8”)

Longitudinal Facial Cracking

100 mm

OuterFlat

InnerCurve

OuterCurve

InnerFlat

InnerCurve

OuterCurve

OuterFlat

I IIIII IV V

Plant Experience I

• Inside curve region

Plant Experience III

• Short jagged cracks form all around perimeter

I IIIII IV V

• Inside curve region

• Long cracks in root of depression

• Caused about 60% of breakouts

Plant Experience II

• Short, jagged cracks form all around perimeter

• Heat transfer related

Plant Experience IV

• Occur around SEN- fluid flow problems


Plant Experience II

• Outside curve region

• Long cracks in root of depression

Occur around SEN fluid flow problems

Plant Experience V

• Off-corner on wide face- insufficient taper

Plant Experience I:LFC Breakout Locations

22Inner Flat Inner Curve Outer Curve Outer Flat

LFC Breakout LocationsData provided by A. Kamperman of Corus

16

18

20

ak

ou

ts (

%) Inner Flat Inner Curve Outer Curve Outer Flat

750 mm Outer Funnel Width

10

12

14

tal L

FC

Bre

a

January 2005 - August 2007

4

6

8

nta

ge

of

To

t

0

2

4

0 100 200 300 400 500 600 700

Pe

rce

n


Distance from Center (mm)

Each interval is 10 mm. Shows the locations of depression-type LFC’s that caused breakouts

Longitudinal Facial Cracking: Depression Mechanism (Type I,II)

• Root cause is non-uniform heat transfer• Initiate nonuniformity (shell depression)

Depression Mechanism (Type I,II)

Initiate nonuniformity (shell depression)– Variations in slag rim thickness at meniscus– Gap from necking (self-correcting)– Gap from buckling (self-amplifying)Gap from buckling (self amplifying)

• Depression causes:– Lower heat flux

Hi h h ll t tAmplifiesif b kli

Mo

ld W

Mo

ld W

– Higher shell temperature– Thinner shell– Grain growth (larger grains)

M b ittl b h i

if buckling

Wall

Wall

– More brittle behavior– Stress and strain concentrations

• Tensile inelastic strain exceeds critical

Combination causes cracks


value cracks form

Numerical Model

• Coupled thermal-stress analysis with ABAQUS– Transient solidification heat transfer in a moving 2D sliceTransient solidification heat transfer in a moving 2D slice – Special two-level integration scheme for elastic-viscoplastic

mechanical behavior (implemented with a UMAT user subroutine)

• Thermal analysis: H∂Thermal analysis:– Standard Fourier heat conduction with solidification– Temperature-dependent thermal conductivity and specific heat

• Mechanical analysis:

( )HT

tρ ∂ = ∇ ⋅ ⋅∇

∂k

• Mechanical analysis:– Standard mechanical (static) equilibrium, small strains– Temperature- and phase- (L, δ, γ) dependent constitutive behavior

T d d l i d l d h l i

0∇ ⋅ + =σ b

– Temperature-dependent elastic modulus and thermal expansion– “Softened” exponential pressure-overclosure contact relationship– Interfacial friction factor of µ = 0.16 [Meng et al., CMQ 45-1 pg. 79-94]


– Ferrostatic pressure

• 2D model includes the funnel shape and mold oscillations

0.045 %C Steel Phases

1500

1600

0 9

1.0

1300

1400

1500

C) 0.7

0.8

0.9

(--) Fraction α

1000

1100

1200

pe

ratu

re (

ºC

Liquidus temperature 1530.45 ºCSolidus temperature 1507.51 ºC

0 4

0.5

0.6

se F

ractio

n

Fraction δ

Fraction γ

Fraction L

800

900

1000

Te

mp

0.2

0.3

0.4

Ph

as

600

700

0.0 0.2 0.4 0.6 0.8 1.0 1.2Percent Weight Carbon

0.0

0.1

600 800 1000 1200 1400 1600Temperature (ºC)


Percent Weight Carbon

[Won and Thomas, MTB, 2001]

Temperature ( C)

Constitutive Equations

• Austenite (Kozlowski model III):( ) ( ) ( ) ( ) ( ) ( )3

2

411 4.465 10

s expf T

f T Kf C f Tε σ ε ε −− × =

18

20

Austenite( ) ( ) ( )

( )( )( )

1

31

32

33

s exp

130.5 5.128 10

0.6289 1.114 10

8.132 1.54 10

f C f TT

f T T

f T T

f T T

ε σ ε ε

−

−

−

= − − = − ×

= − + ×

= − ×12

14

16

MP

a)

δ-Ferrite

• δ-ferrite (Zhu modified power law):

( )3

4 4 5 2

8. 3 .5 0

( ) 4.655 10 7.14 10 1.2 10

f

f C C C= × + × + ×

( ) ( ) 5.521 0.1 ( ) 300 (1 1000 )n

ms f C Tε σ ε−− = +6

8

10

Str

es

s (

M

Strain Rate = 10-4 s-1

Temperature = 1400 °CComposition = 0.045 %wt C ( ) ( )

( ) ( )25.56 104

5

4

0.1 ( ) 300 (1 1000 )

1.3678 10

9.4156 10 0.34951 1.617 10 0.06166

s f C T

f C C

m T

n T

ε σ ε−− ×

−

−

+

= ×

= − × += × −0

2

4

• Liquid and mushy zone:– Treat as low yield stress, low elastic

modulus perfectly plastic solid

0 1 2 3 4 5 6 7 8 9 10

Strain (%)

• P.F. Kozlowski, B.G. Thomas, J.A. Azzi, and H. Wang, “Simple Constitutive Equations for Steel at High Temperature.” Metallurgical and Materials T ti 23A (1992) N 3 903 918


modulus, perfectly-plastic solid

T in Kelvin, σ in MPa, C in weight % C

Transactions, 23A (1992), No. 3, pg. 903-918.

• H. Zhu, “Coupled Thermo-Mechanical Finite-Element Model with Application to Initial Solidification.” Ph.D. Thesis, University of Illinois at Urbana-Champaign, (1996).

Evaluation of Kozlowski Model

80

90

+10%

+20%

+30%

+40%

+50%

24

27

30

0.005 %C

0.051 %C

40

50

60

70

Str

ess

(MP

a)

-10%

-20%

0%

15

18

21

24

Str

ess

(MP

a)

0.290 %C

0.460 %C

0.710 %C

0.930 %C

1.240 %C

10

20

30

40

Cal

cula

ted

Wray Data

6

9

12

15

Cal

cula

ted

S 1.540 %C

0

10

0 10 20 30 40 50 60 70 80 90

Measured Stress (MPa)

0

3

0 3 6 9 12 15 18 21 24 27 30

Measured Stress (MPa)

Kozlowski Model is generally accurate, except for:

• Low stress, high strain

±10%: 46% of data

±20%: 75% of data


• High stress, low strain

Traveling Slice Analysis


Finite Element Mesh

Solidifying Steel Computational DomainSolidifying Steel

Mold

Computational Domain

Near inside of funnel

Corner

• Standard 4-node heat transfer elements

• Hybrid formulation of generalized plane strain mechanical elements


strain mechanical elements

• Fixed mesh, about 60000 nodes

Process Parameters

Casting speed 5.5 m/min

Carbon content 0.045 %wt

217 ipm

Pour temperature 1545.0 ºC

Strand width 1200 mm

2813 ºF

47”Strand width 1200 mm

Narrow face taper 1.0 %/m

47

Meniscus depth 104.2 mm

Time in mold 10.86 s

4”


Heat Flux Profiles:Interfacial Thermal Boundary ConditionInterfacial Thermal Boundary Condition

• Heat flux uniformly applied around most of the perimeterD h t fl t t

8

0.0 2.2 4.4 6.6 8.8 11.0

Time Below Meniscus (s)

• Decrease heat flux at corner to account for gap formation(linear drop to 50% over 20 mm)

• Average Q matches measurements4

5

6

7

x (

MW

/m²)

Q = 6.5*(t(s)+1.0)-0.5

Qavg = 2.92 MW/m²Average Q matches measurements

1

2

3

4

He

at

Flu

x

3.25

3.50

m²)

Simulated case

2.92 MW/m2

0

0 200 400 600 800 1000Distance Below Meniscus (mm)

2.75

3.00

e H

ea

t F

lux

(M

W/m

100%

20 mm 2.00

2.25

2.50

Av

era

ge

New Plates Old Plates

CON1D New Plates CON1D Old Plates

Log. (New Plates) Log. (Old Plates)


100% 50%

20 mm 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00

Casting Speed (m/min)

[Santillana et al., AISTech 2007]

Ferrostatic Pressure and Mold Wall Movement:Mechanical Boundary Conditionsy

Time Below Meniscus (s) Time Below Meniscus (s)

70

80

0.0 2.2 4.4 6.6 8.8 11.0

Time Below Meniscus (s)

12

14

)

0.0 2.2 4.4 6.6 8.8 11.0Time Below Meniscus (s)

Wide Face

Narrow Face

40

50

60

su

re (

kP

a)

6

8

10

ce

me

nt

(mm

10

20

30

Pre

ss

Delayed about one second to allow the outermost row of elements to solidify

2

4

6

Dis

pla

c

0

0 200 400 600 800 1000

Distance Below Meniscus (mm)

of elements to solidify

0

0 200 400 600 800 1000



Hot Face DisplacementFerrostatic Pressure

Model Verification:Properties, Parameters, and Boundary Conditionsp y

Insulated ed

Thermal Boundary Conditions• J.H. Weiner and B.A. Boley, “Elasto-Plastic Thermal Stresses

in a Solidifying Body.” Journal of the Mechanics and Physics of Solids, 11 (1963), No. 3. pg 145-154.

Property/Condition Value

Density 7500.0 kg/m3

Specific heat 661.0 J/(kg·ºC) Prescribed temperatureor heat flux

Insulated

Insulated Insu

late

Latent heat 272.0 kJ/kg

Thermal conductivity 33.0 W/(m·ºC)

Thermal expansion coefficient 20.0E-6 m/(m·ºC)

Poisson’s ratio 0 3 Fre

eZero perpendicular displacement

Mechanical Boundary Conditions

Poisson s ratio 0.3 --

Initial temperature 1495.0 ºC

Liquidus temperature 1494.48 ºC

Solidus temperature 1494.38 ºC

Str

ess-

F

Equal perpendicular displacement

Zero perpendicular di l t

Solidus temperature 1494.38 C

Mold temperature 1000.0 ºC

Yield stress at mold temp. 20.0 MPa

Yield stress in liquid material 35.0 kPaDomain

Solid materialdisplacement


Elastic modulus in solid 40.0 GPa

Elastic modulus in liquid 14.0 GPaLiquid material

Model Verification:Temperature SolutionTemperature Solution

1400

1450

1500

1200

1250

1300

1350

mp

erat

ure

(ºC

)

1050

1100

1150

1200

Tem

Analytical

Numerical

2 s10 s30 s

1000

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30

Distance From Shell Surface (mm)


Model Verification:Stress SolutionStress Solution

4

6

8

10

12

-6

-4

-2

0

2

tres

s (M

Pa)

-16

-14

-12

-10

-8St

Analytical

Numerical

2 s10 s30 s

-20

-18

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0



Temperature Results

Slight two-dimensional heat transfer in funnel transition region

Inner Curve Outer CurveInner Curve Outer Curve

SolidusSolidus

9.6 mm


t = 10.86 s (mold exit)

Temperature Solution

1600L

1500δ

L + δ

δ + γ

2 s 4 s 6 s 8 s 10 s

1300

1400

era

ture

(ºC

)

γδ γ

1200Te

mp

e

1000

1100

0 2 4 6 8 10 12 14 16


0 2 4 6 8 10 12 14 16

Distance Beneath Shell Surface (mm)

Stress Profiles and HistoriesThrough Thickness in Flat RegionsThrough Thickness in Flat Regions

2

4

62 s

4 s 6 s 8 s 10 s

Tensile Stress

• After initial tensile load, surface stays in compression

-4

-2

0

Str

es

s (

MP

a)

Compressive Stress

stays in compression

• Solidification front is always under tensile loading

• Net stress through-thickness is

6

-12

-10

-8

-6 • Net stress through-thickness is always zero

• Soft delta-ferrite unable to carry a substantial load

-2

0

2

4

s (

MP

a)

0.0mm 1.5mm 3.0mm 4.5mm 6.0mm 7.5mm

0 2 4 6 8 10 12 14 16

Distance Beneath Shell Surface (mm)

substantial load

• Stress peaks after transition to the austenite phase

• By mold exit only the first 2 mm of-10

-8

-6

-4

Str

es

s


• By mold exit, only the first 2 mm of the shell are in compression

-12

0 1 2 3 4 5 6 7 8 9 10 11Time (s)

1.5 mm = 0.06”

Surface Stress Around Perimeter:Effect of Funnel Width

8.0750 mm Outer Funnel Width950 O t F l Width

Effect of Funnel Width

4.0

MP

a)


2 s

-4.0

0.0

ce S

tres

s (M

-8.0

Sh

ell

Su

rfac

4 s

6 s

8 s

-16.0

-12.0

S

10 s


0 50 100 150 200 250 300 350 400 450 500 550 600 650

Distance from Mold Centerline (mm)

Stress Near Solidification Front:Effect of Funnel Width

8.0750 mm Outer Funnel Width950 mm Outer Funnel Width

Effect of Funnel WidthPeak stress (in γ phase)

6.0

7.0(M

Pa)


4.0

5.0

hel

l S

tres

s

4 s

6 s

2.0

3.0

Max

imu

m S

h

8 s

0.0

1.0

M 2 s

10 s


0 50 100 150 200 250 300 350 400 450 500 550 600 650


Funnel Bending Effect

• A unique attribute of funnel molds is that the steel h ll i i ifi tl b t it lid d th ldshell is significantly bent as it slides down the mold

Tension

Compression

Compression

TensionCompression

• Beam theory from solid mechanics can elucidate the important parameters in the phenomenon

y

x2·h

This end pinned, u = 0M

εmax, compressive

εmax, tensile

x

y

Rε = −


w

εmax, compressive R

[R.C. Hibbeler, Mechanics of Materials, 5e, 2003]

Analytical Bending Model:Comparison with Numerical ModelComparison with Numerical Model

• Take the difference between bending a beam to Time Below Meniscus (s)between bending a beam to the funnel radius at the meniscus and the funnel radius at some other depth:

0.60

0.70

rain

(%

)

0.0 2.2 4.4 6.6 8.8 11.0

Analytical ModelNumerical Model

radius at some other depth:

( ) ( )( )

( )( ) ( ) ( ) ( )

( ) ( )meniscus

bendingmeniscus meniscus

z z r z r zz z

r z r z r z r z

δ δε δ

−= − =

0.30

0.40

0.50

Be

nd

ing

Str

750 mm OuterFunnel Width

δ = distance from neutral axis ≈ shell thickness0.10

0.20

Me

ch

an

ica

l B

En

d o

f fu

nn

el l

en

gth


( )2( )( )

4 16 ( )outer funnel width inner funnel widthcrown z

r zcrown z

−= +

⋅

• Compare with results of 2D model with the thermal

0.00

0 200 400 600 800 1000

M



model with the thermal effects subtracted

Bending Strain on Solidification Front

Analytical Bending ModelLarger total funnel width = Larger radius = Lower bending strain and strain rate

Shallower funnel = Larger radius = Lower bending strain and strain rateLonger Funnel = Increases strain near bottom of funnel (larger radius for more time), but lowers strain rate

0 40

0.50

0.60

0.70

0.80750 mm Outer Funnel Width850 mm Outer Funnel Width950 mm Outer Funnel Width

nd

ing

Str

ain

(%

)

0 40

0.50

0.60

0.70

0.80260 mm Inner Funnel Width130 mm Inner Funnel Width0 mm Inner Funnel Width

nd

ing

Str

ain

(%

)

0 50

0.60

0.70

0.80

0.90

1.00

30 mm Crown at Top20 mm Crown at Top10 mm Crown at Top

nd

ing

Str

ain

(%

)

En

d o

ffu

nn

el l

en

gth

0 40

0.50

0.60

0.70

0.80

nd

ing

Str

ain

(%

)

130 mm InnerFunnel Width


8 mm Crownat Bottom

0.00

0.10

0.20

0.30

0.40

En

d o

ffu

nn

el l

en

gth

Me

ch

an

ica

l B

en

0.00

0.10

0.20

0.30

0.40

En

d o

ffu

nn

el l

en

gth

Me

ch

an

ica

l B

e

0.00

0.10

0.20

0.30

0.40

0.50

Me

ch

an

ica

l B

e

0.00

0.10

0.20

0.30

0.40

850 mm Funnel Length



Me

ch

an

ica

l B

e

0.00


0.10

0.12

0.14

750 mm Outer Funnel Width850 mm Outer Funnel Width950 mm Outer Funnel Width

thn R

ate

(%

/s)


0.10

0.12

0.14260 mm Inner Funnel Width130 mm Inner Funnel Width0 mm Inner Funnel Width

thn R

ate

(%

/s)


0.12

0.15

n R

ate

(%

/s)

En

d o

fn

ne

l le

ng

th

0.10

0.12

0.14

850 mm Funnel Length950 mm Funnel Length1050 mm Funnel Length

n R

ate

(%

/s)


0.04

0.06

0.08

0.10

En

d o

ffu

nn

el l

en

gt

an

ica

l B

en

din

g S

tra

in

0.04

0.06

0.08

0.10

En

d o

ffu

nn

el l

en

gt

an

ica

l B

en

din

g S

tra

in

0.03

0.06

0.09

30 mm Crown at Top20 mm Crown at Topa

nic

al

Be

nd

ing

Str

ain fun

0.04

0.06

0.08

0.10

an

ica

l B

en

din

g S

tra

in


0.00

0.02


Me

ch

a

0.00

0.02


Me

ch

a

0.00

0 200 400 600 800 1000

10 mm Crown at Top


Me

ch

a

0.00

0.02


Me

ch

a

Subsurface Hot Tears

• Typical solidification stresses put tension on the solidification frontsolidification front– Tension increased by bending effect in inner curve

region, thus higher risk of hot tearingg g g

• Critical hot tearing strain quantified by Won:0.02821=ε Won et al Metall Mat Trans 31B:4 (2000) pg 779

• Brittle temperature zone (BTZ):

0.3131 0.8638=⋅Δc

BTε

εWon et al., Metall. Mat. Trans., 31B:4 (2000), pg. 779

• Average inelastic strain rate in BTZ:

( 99%) ( 90%)B s sT T f T fΔ = = − =


( 99%) ( 90%)( 99%) ( 90%)

s s

s s

f f

t f t f

ε εε = − === − =


• Extremely fine mesh required to apply Won model (0 06 mm element size is insufficient)(0.06 mm element size is insufficient)– Use 1D numerical model to calculate temperatures and

inelastic strain profile history in flat regions of moldp y g

– Add bending effect with analytical model

• Low-carbon steels exhibit strong numerical noise– Use a higher carbon grade (0.07%C) to reduce effect

– High-carbon grades are also more crack-sensitive

• Define “damage index” as ratio of actual damage strain to critical damage strain (crack forms at unity)


dmg cD ε ε=( 99%) ( 90%)dmg s sf fε ε ε= = − =


• No hot tears will form under normal operation 0.20

0.25

e (%

/s)

Parallel MoldNominal Funnel Mold200 mm Wider Funnel100 mm Longer Funnel

0.10

0.12

)

– Bending effect increases likelihood of cracks

• Most likely place is just a 0 05

0.10

0.15

Inel

asti

c S

trai

n R

ate

0.04

0.06

0.08

Dam

age

Str

ain

(%

)

Parallel MoldNominal Funnel Mold200 Wid F l

y p jfew mm subsurface

• Funnels more susceptible to hot tears:

0.00

0.05

0 1 2 3 4 5 6 7


Avg

.

0.00

0.02

0 1 2 3 4 5 6 7


200 mm Wider Funnel100 mm Longer Funnel

susceptible to hot tears:– Narrower funnel width

(higher bending strain)– Deeper crowns (higher

2.00

2.50

3.00

Str

ain

(%

)


0.06

0.08

0.10

dex

(--

)

Deeper crowns (higher bending strain)

– Longer (higher strain rate when mushy zone is

0.50

1.00

1.50

Wo

n C

riti

ca

l S

0.02

0.04

Dam

age

Ind



large) 0.00

0 1 2 3 4 5 6 7


0.00

0 1 2 3 4 5 6 7


Pushing the Shell

• As the crown decreases, the steel shell is pushed i d t th SEN d t d t th finward to the SEN and outward to the narrow faces– Opposed by friction and excessive narrow-face taper

Affected by solidification shrinkage (possibly– Affected by solidification shrinkage (possibly compensating)

– Most noticeable at early times before opposing effects y pp gare strong, but always present

D i O d b f i tiDecreasing crown

Shell pushed “uphill”

Opposed by friction


Shell pushed uphill by funnel

Interfacial Gaps

• Predicted gaps are mechanical effects, due to no coupling of mechanical model to heat transfer model (coupled model would have larger gaps)model to heat transfer model (coupled model would have larger gaps)

• Small gaps in the inner curve region– “Shell pushing” encourages good contact

• Larger gaps in the outer curve regionT

C

T• Larger gaps in the outer curve region– Shrinkage from outer flat region is resisted by “shell pushing”

• Both influenced by bending effect

Sh i k i “ hi ” t h i th iddl f th f l

CT

• Shrinkage minus “pushing” meets somewhere in the middle of the funnel

0.040

0.050

p (

mm

)

6 9 10 86

Inner Flat Inner Curve Outer Curve Outer Flat

0.010

0.020

0.030

terf

ac

ial G

ap 6 s 9 s 10.86 s


0.000

0 100 200 300 400 500 600

Distance from Centerline (mm)

Int

Depression Mechanisms• Inside curve:

– Friction + bending pins the shell at the transition pointsM ld i d b kli if l l h ll h i k i t h t t h th– Mold may induce buckling if local shell shrinkage is not enough to match the mold perimeter length change

• Outside Curve 1

2

3

• Outside Curve– Friction + bending pins the shell at the inside/outside curve transition point– Excessive NF taper causes the shell to lift off the mold surface, reducing

heat transfer

1

– Bending (funnel and ferrostatic pressure) causes tensile stress on surface, leads to necking


Tangential Displacement

• Project the incremental displacement vector onto a vector tangent to the mold surfaceonto a vector tangent to the mold surface– Neglects the “global” mold displacement, but

includes the effects of the shell sliding around theincludes the effects of the shell sliding around the funnel “corners”

Shellux

uyu

ty

Moldx t

u’x


Surface Displacement:Effect of Funnel Width

0.0

0.5

Effect of Funnel Width

-1.5

-1.0

-0.5

0.0

nt

(mm

)

2 s

-3.0

-2.5

-2.0

isp

lace

men

2 s

-4.5

-4.0

-3.5

ng

enti

al D

i

6 s

-6.0

-5.5

-5.0Ta

750 mm Outer Funnel Width950 mm Outer Funnel WidthParallel Mold

10 s


0 50 100 150 200 250 300 350 400 450 500 550 600 650


Surface Trajectories

• Put markers at the meniscus that draw a line on the mold as they

0

100

0 50 100 150 200 250 300 350 400 450 500 550 600

Distance From Mold Centerline (mm)m

)Parallel Mold, no Friction

line on the mold as they move with the shell

• Friction plays a very important role on shell

100

200

300

400

500

600elo

w M

enis

cus

(mm

important role on shell shrinkage (1D heat transfer model is insufficient to predict mold tapers)

600

700

800

900

1000

Dis

tan

ce B

e

20x Magnified Displacement

0

100

200

0 50 100 150 200 250 300 350 400 450 500 550 600

Distance From Mold Centerline (mm)

s (m

m)

p )

• Friction holds the shell in place at early times by overpowering

Parallel Mold, with Friction

300

400

500

600

700

nce

Bel

ow

Men

iscu

s y p gshrinkage


800

900

1000

Dis

tan


Surface Trajectories

• Inside curve trajectories are spaced further apart ( h i ki h

0

100

0 50 100 150 200 250 300 350 400 450 500 550 600


m)

Parallel Mold, with Friction

(not shrinking as much as it wants too)

• Outside curve trajectories are spaced

200

300

400

500

600elo

w M

enis

cus

(mm

closer together (shrinking more than it wants to)

• Outside curve shows

600

700

800

900

1000

Dis

tan

ce B

e


initial movement towards the narrow face

• Large gap at inside/outside transition

0

100

200

0 50 100 150 200 250 300 350 400 450 500 550 600


s (m

m)

Funnel Mold, with Friction

inside/outside transition suggests outside curve bending + friction pulls the shell towards the narrow faces

300

400

500

600

700

nce

Bel

ow

Men

iscu

s


narrow faces800

900

1000

Dis

tan


Conclusions• A larger funnel radius provides:

– More uniform heat transfer– Smaller bending effect in the transition region– Lower tendency to form subsurface hot tears

• A “better” funnel (with respect to depression type• A better funnel (with respect to depression-type LFCs) has a wide funnel and small crown

D

Increase outer funnel widthDecrease crown funnel width

• Depression-related LFCs are also affected by f i ti d f t

Decrease inner funnel width


friction, and narrow-face taper• Many other phenomena can cause LFCs

Acknowledgements

• Continuous Casting Consortium Members (ABB, Arcelor-Mittal, Baosteel, Corus, Delavan/Goodrich,(ABB, Arcelor Mittal, Baosteel, Corus, Delavan/Goodrich, LWB Refractories, Nucor, Nippon Steel, Postech, Steel Dynamics, ANSYS-Fluent)

• Dr. Seid Koric, Dr. Chunsheng Li, Dr. Hong Zhu

• Begoña Santillana, Gert Abbel, Arnoud Kamperman, Jean Campaniello, Frank Grimberg

• National Center for Supercomputing Applications (NCSA) at UIUC – “Tungsten” and “Abe” clusters


• Dassault Simulia, Inc. (ABAQUS parent company)

uiuc, august 5, 2009 thermal-mechanical behavior of the

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