14 SHI Ge Thermal-Mechanic Behavior Shell BeamBlankMold...

ANNUAL REPORT 2008ANNUAL REPORT 2008UIUC, August 6, 2008

Thermal-mechanical Behavior of The

Solidifying Steel Shell in A Beam blankSolidifying Steel Shell in A Beam-blank

Mold and Ideal Taper Design

Ge Shi

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign

Outline

• Background

• Objective

• Model Description

• Result• Result– Temperature

– Shell Thickness

– Interfacial gap formation

– Stress

– Effects of mold distortionEffects of mold distortion

• Taper Improvement

• Conclusion

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ge Shi 2

Background

By L. C. Hibbeler S. KORIC, B. G. THOMAS, K. XU, and C. SPANGLERIn Thermo-Mechanical Modeling of Beam Blank Casting


g g

Objective

• Simulate thermal-mechanical behavior of the shell in a beam blank mold including:shell in a beam-blank mold, including:– Temperature

– Shell thickness

– Interfacial gap formation

– Stress

– Effects of mold distortionEffects of mold distortion

• Suggest an improved taper


Mold Top View

Mold wide face(i id di )

436

(inside radius)

Flange corner

Flange tip

93mm

436mm

WebMold narrow

facex

y

Shoulder

g p

Annular cooling-Pour Annular coolingwater slotfunnel

Mold wide face(inside radius)

576mm


By L. C. Hibbeler S. KORIC, B. G. THOMAS, K. XU, and C. SPANGLER in Thermo-Mechanical Modeling of Beam Blank Casting

576mm

Model Domain

Refined section for solidifying shell

Coarse section for liquid

40 [

mm

]

Domain of the Model Mesh


Heat Transfer Model Eqs.

( )H T∂

• Governing equation

( ) ( )( )H Tk T T

Tρ

∂= ∇ ⋅ ∇

∂

ˆT T( t)= x

• Boundary conditions:

T T( , t)= x

( ) ˆk T q( , t)− ⋅ =n x∇

( )k T h(T T )∞− ⋅ = −∇ n


• By S. KORIC, B. G. THOMAS, K. XU, and C. SPANGLER In Thermo-Mechanical Model of Continuous Casting of Steel Beam Blanks: Part I Model Formulation and Validation

Mechanical Model Eqs.

1 T∇∇ ˆ A

• Governing equation • Boundary conditions:

])([2

1 Tuu ∇+∇=ε

( ) 0x b∇ ⋅ σ + =u on A

on AΦ

=⋅ =

u u

nσ Φ

• Constitutive equation

thieel εεεε ++=

ie th:( )= − −Dσ ε ε ε

Total strain rate:

Total stress rate:

B

22 (k )

3= μ + − μ ⊗D I I I

Isotropic elasticity tensor :



Boundary Condition

•Surface behavior [DISP]

Thermal distortion

•Contact [GAPCON]

N l b h i –Thermal distortion

–Mold taper

•UMAT

–Normal behavior

–Thermal conductance

•Surface load [DLOAD]


–Material properties

–Mushzone specification

–Ferrostatic pressure

Interface Heat Flux

( )"q (h h ) T T= − + −• Water ( )gap c rad shell moldq (h h ) T T= +

Conduction

• Water

• mold

• Powder

powair

c mold air pow shell

dd1 1 1

h h k k h= + + +

• Air gap

• Shell

( )( )8

2 25.67 10h T T T T

−×= + +

Radiation

( )( )rad shell mold shell mold

m s

h T T T T1 1

1= + +

+ −ε ε



Model Description________________________________________________________________________

Casting strand [mm] 576 x 436 x 93

W ki M ld l th [ ] 660 4Working Mold length [mm] 660.4

Total taper at flange [mm] 2.33

Total taper at sloped shoulder edge [mm] -2.22

Total taper at wide face [mm] 0.48

T t l t t f [ ] 3 0Total taper at narrow face [mm] 3.0

Type of taper Parabolic

Mold contact resistance feat coefficient, hmold [W/m2/K] 2500

Casting speed [m/min] 0.889

M ld Th l C d ti it (C ) [W/ K] 370Mold Thermal Conductivity (Copper) [W/mK] 370

Steel grade [%C] 0.071

Initial temperature strand [C] 1523.70

Initial temperature mold [C] 285

Li id [C] 1518 70Liquidus temperature [C] 1518.70

Solidus temperature [C] 1471.95

________________________________________________________________________

By Koric et al, Int J Num Meths Eng., 2007


y , g ,

Coefficients for Gap Heat Flux

hmold = 2500 W/m2

kair=0.06 W/mK

dpow=0.1mm

Temperature, oC hshell, W/m2K

1030 1000 1150 2000 p

kpow=1 W/mK 1518 10,000

1530 20,000

m s 0.8ε = ε =

J. K. Park, B. G. Thomas, and I. Samarasekera: Ironmaking and Steelmaking, 2002

H H N J E L T J Y Y M W K Ki K H Oh d J K Y ISIJ I t ti l


Han, H. N., J. E. Lee, T. J. Yeo, Y. M. Won, K. Kim, K. H. Oh and J. K. Yoon: ISIJ International

Simulation Result


Temperature Results

Temperature Contour of Strand at Temperature Contour of Strand 459 [mm] Below Meniscus

pat 660 [mm] Below Meniscus


Temperature HistoriesTemperature Histories for The Points on Shell Perimeter

Reheating Reheating

11, 12 overlapping


Cooling Rate

291.74 mm Below Meniscus



6 0




Shell Thickness

60

2% Solid

55% S lid 30

35

2% Solid

55% S lid

30

40

50ic

knes

s [m

m]

55% Solid

90% Solid

Meas. Outside Radius

Meas. Inside Radius

15

20

25

30

hic

knes

s [m

m]

55% Solid

90% Solid

Measurements

10

20

Sh

ell

Th

0

5

10

15

Sh

ell

Th

Shell Thickness Along the P i t f th St d 459

Shell Thickness History for The T t P i t th NF 50

0

0 100 200 300 400 500 600 700

Distance Along the Perimeter of Shell [mm]

0

0 100 200 300 400 500 600 700 800

Distance Below Meniscus [mm]

Perimeter of the Strand 459 mm Below Meniscus

Test Point on the NF 50 mm from the RFL Corner 459 mm Below Meniscus


Gap Location & Size: Shoulder Region459 mm Below Meniscus

G t E d Sh ld

459 mm Below Meniscus

These gaps are responsible for h ll thi i d ti Gap at End Shouldershell thinning, and sometimes

break-outs at shoulder

Gap at Mid Shoulder


Gap Location & Size: Flange Region459 mm Below Meniscus459 mm Below Meniscus

Gap Opening at Left and Right Corner

(No shell thinning due to 2 D heat transfer in corner)


(No shell thinning due to 2-D heat transfer in corner)

M/S Behavior & Gap SizeGap Size

Web Region

Positive Displacement = towards steel

Gap Size

Slant region


M/S Behavior & Gap SizeGap Size

Flange region

Positive Displacement = towards steel

Gap Size

NF region


Tangential Displacement

Web region Slant region

Positive Displacement p= Away from Point 10 towards centerline

NF regionFlange region


Stress

Maximum Principal Stress Contour 459 mm Below Meniscus

Maximum Principal Stress Contour 660 mm Below Meniscus459 mm Below Meniscus Contour 660 mm Below Meniscus


Effects of Mold Distortion

Web region Slant region

NF regionFlange region

10,11,12 Overlapping


Taper Analysis

• Shoulder Gap Formation Mechanisms

Slant region

Mechanisms– Too much flange taper (A):

pushing shell along slant, causing buckling at shoulderg g

– Too much negative taper of B’

TT

AWB’


B

B’

Taper Improvement

T• Keep taper on Aunchanged

AW

• Increase taper on W by 0.3 mm at the bottom

• Increase taper on B by 0 4 t th b tt

B

B’

0.4 mm at the bottom

• Decrease taper on B’ by 0.8 mm at the bottom

• Increase taper on T by B• Increase taper on T by 0.3 mm at the bottom

NF region (B)Flange region (A)Web region (W) Slant region (T, B’)


Improved Taper Recommendations

7

8

Original Taper on A

Original Taper on B

Original Taper on W

Original Taper on T2.5

3

Original Taper

Improved Taper on A

Improved Taper on B

4

5

6

Tap

er*

[mm

]Original Taper on T

Original Taper on B'

Improved Taper on A

Improved Taper on B

Improved Taper on W

Improved Taper on T

Improved Taper on B'1.5

2

per

[%

/m]

Improved Taper on W

Improved Taper on T

Improved Taper on B'

1

2

3

To

tal

T

0.5

1

Tap

0

0 100 200 300 400 500 600 700 800


( )1000 / %

2topD D z

Taper mm mD

−= ×( )topTaper D D z= −

0

0 100 200 300 400 500 600 700 800


2 bottom

pz D⋅ ⋅


*Note: total taper includes both sides of the mold for A, B, W, and B’D = A, B, W, T, or B’

Summary of Taper

Original Improved

Top [mm] Bottom [mm] Taper [ %/m] Top [mm] Bottom [mm] Taper [ %/m]

A 436.336 430.530 0.948167 436.336 430.530 0.948167

B 576.633 568.960 0.948159 576.633 568.545 1.000168

W 93.447 92.202 0.949003 93.447 91.890 1.190932

T 70.536 69.596 0.949357 70.536 69.284 1.270224

B’ 323.069 318.770 0.948036 323.069 319.601 0.762780

• Increase Taper B to decrease the right corner gap in x direction• Increase Taper B to decrease the right corner gap in x direction

• Increase Taper W to decrease the shoulder gap in y direction

• Increase Taper T decrease the corner gaps in x direction

• Decrease Taper B’ to decrease the shoulder gap by lessening• Decrease Taper B to decrease the shoulder gap, by lessening tangential sliding around corner

• Keep Taper A unchanged to balance between enlarging corner gaps in y direction (if too small) and pushing the shell tangentially along


y ( ) p g g y gslant (if too large).

Conclusion

• Four gaps are predicted along the mold / shell perimeter: the middle and end of shoulder and at both flange corners.the middle and end of shoulder and at both flange corners.

• Heat transfer at gap locations slows down, causing reheating especially at the shoulder where the local shellreheating, especially at the shoulder, where the local shell thickness is reduced dangerously. (Flange corners stay thick owing to 2-D heat transfer.)

• The thermal distortion has a minor but significant effect half-way down mold, where it is maximum.

• An improved taper design is proposed.


Acknowledgements

• Professor Brian. G. Thomas, Seid Koric, Lance Hibbeler

• Continuous Casting Consortium Members (Nucor, Postech, LWB Refractories, Corus, Labein, Arcelor-Mittal, Baosteel, Steel Dynamics, Postech, ANSYS)Baosteel, Steel Dynamics, Postech, ANSYS)

• National Science Foundation

• National Center for Supercomputing Applications (NCSA) at UIUC

• HKS (ABAQUS)


14 SHI Ge Thermal-Mechanic Behavior Shell BeamBlankMold...

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