University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 1
Chunsheng Li
Department of Mechanical & Industrial EngineeringUniversity of Illinois at Urbana-Champaign
October 18, 2001
Chunsheng Li
Department of Mechanical & Industrial EngineeringUniversity of Illinois at Urbana-Champaign
October 18, 2001
Maximum Casting Speed for Continuous Casting Steel Billets
Maximum Casting Speed for Continuous Casting Steel Billets
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 2
ObjectiveObjective
Analyze bulging below the mold for unsupported billet bloom casting due to ferro-static pressure for different casting speeds.Determine critical casting speed to avoid cracks as a function of section size and mold length.
Analyze bulging below the mold for unsupported billet bloom casting due to ferro-static pressure for different casting speeds.Determine critical casting speed to avoid cracks as a function of section size and mold length.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 3
Model DescriptionsModel Descriptions
Finite element thermal stress modelPhase fractions from non-equilibrium Fe-C phase diagram for plain carbon steelRecalescence and kinetics neglectedLinear phase fraction model between liquidus and solidus for ferritic and austenitic stainless steels2-D generalized plane strain
Finite element thermal stress modelPhase fractions from non-equilibrium Fe-C phase diagram for plain carbon steelRecalescence and kinetics neglectedLinear phase fraction model between liquidus and solidus for ferritic and austenitic stainless steels2-D generalized plane strain
flowthermalcreepplasticelastictotal εεεεε &&&&& +++= /
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 4
Heat Transfer Model ValidationHeat Transfer Model Validation
• Lines: Boley & Weiner’s analytical solution*• Symbols: CON2D computation results
* J. H. Weiner and B. A. Boley, J. Mech. Phys. Solids, 1963, Vol. 11, pp145-154
Distance from Slab Surface (mm)
Tem
per
atu
re(C
)
0 10 20 301000
1100
1200
1300
1400
1500
5 sec.5 sec.10 sec.10 sec.15 sec.15 sec.20 sec.20 sec.25 sec.25 sec.30 sec.30 sec.35 sec.35 sec.43 sec.43 sec.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 5
Stress Model ValidationStress Model Validation
• Lines: Boley & Weiner’s analytical solution*• Symbols: CON2D computation results
* J. H. Weiner and B. A. Boley, J. Mech. Phys. Solids, 1963, Vol. 11, pp145-154
Distance from Slab Surface (mm)
YS
tres
s(M
Pa)
0 10 20 30-25
-20
-15
-10
-5
0
5
10
15
5 sec.5 sec.10 sec.10 sec.15 sec.15 sec.20 sec.20 sec.25 sec.25 sec.30 sec.30 sec.35 sec.35 sec.43 sec.43 sec.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 6
Steel Properties AssumedSteel Properties Assumed
Mizukami elastic modulus dataTemperature dependent conductivity, enthalpy and thermal linear expansion.Kozlowski constitutional equations for austenite, and modified model for delta-ferrite: – Kozlowski Model for Austenite – Modified Power Law Model for δ-ferrite
Mizukami elastic modulus dataTemperature dependent conductivity, enthalpy and thermal linear expansion.Kozlowski constitutional equations for austenite, and modified model for delta-ferrite: – Kozlowski Model for Austenite – Modified Power Law Model for δ-ferrite
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 7
Constitutive Model Constitutive Model
0.1
1
10
1200 1250 1300 1350 1400 1450 1500 1550
dε/dt 2.8e-5 s-1
dε/dt 2.3e-2 s-1
ELEC FEFE-0.028CFE-0.044CFE-3.0SI
Temperature (Degree C)
Wray Data
Constitutive Model
γ δ+γ
δ+
δ
L
10% δ
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 8
Non-equilibrium phase diagram* of plain carbon steels** used in CON2DNon-equilibrium phase diagram* of plain carbon steels** used in CON2D
1300
1350
1400
1450
1500
1550
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Carbon content (%)
Tem
pera
ture
(C)
LL+δ
δ L+δ+γ
δ+γ L+γ
γ
• *Young Mok WON et. al., Effect of Cooling Rate on ZST, LIT, ZDT of Carbon Steels Near Melting Point”, ISIJ International, Vol. 38, 1998, No. 10, pp. 1093 –1099
• **Other Steel Components: 1.52%Mn, 0.34%Si, 0.015%S, 0.012%P
• *Young Mok WON et. al., Effect of Cooling Rate on ZST, LIT, ZDT of Carbon Steels Near Melting Point”, ISIJ International, Vol. 38, 1998, No. 10, pp. 1093 –1099
• **Other Steel Components: 1.52%Mn, 0.34%Si, 0.015%S, 0.012%P
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%
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 9
ConductivityConductivity
Temperature (oC)
Co
ndu
ctiv
ity(W
/mK
)
800 1000 1200 1400 160028
29
30
31
32
33
34
35
36
37
38
39
40
* No enhancement of conductivity in
liquid
* No enhancement of conductivity in
liquid
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 10
EnthalpyEnthalpy
Temperature (oC)
En
thal
py(J
/m3 )
800 1000 1200 1400 16004E+09
5E+09
6E+09
7E+09
8E+09
9E+09
1E+10
1.1E+10
1.2E+10
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 11
Thermal Linear ExpansionThermal Linear Expansion
Temperature (oC)
TLE
(%)
800 1000 1200 1400-0.02
-0.01
0
0.01
0.02
tle(%)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 12
Mold Heat Flux DataMold Heat Flux Data
0
1
2
3
4
5
0 10 20 30 40 50 60
Kapaj [1]
Wolf fitted Eqn for slag casting: 7.3*t(s)-0.5 [2]
Wolf fitted Eqn for oil casting: 9.5*t(s)-0.5 [2]Thin Slab [3]
Brimacombe fitted Eqn: 2.68-0.222t(s) 0.5 [4]
C LI fitted Eqn for Slab casting: 4.05*t(s)-0.33 [5]
C LI fitted Eqn for Billet Casting -4.7556t-0.504
Lorento fitted Eqn: 1.4*Vc(m/min) 0.5 with 700mm Mold [6]Other Sources: 0.1%C, BilletOther Sources- Slab?
Dwell Time (s)[1] Kapaj N., Pavlicevic M. and Poloni A., 84th Steelmaking Conf. Proc., Baltimore, MD, ISS, p67[2] Wolf M.M., I&SM, V.23, Feb., 1996, p47[3] Park J.K., Samarasekera I.V., and Thomas B.G. et al, 83th Steelmaking Conf. Proc., Warrendale, PA, ISS, p13[4] Brimacombe J.K., Canadian Metallurgical Quarterly, V.15, N.2, 1976, p17[5] Li C. and Thomas B.G. Brimacombe Memorial Symposium, Vancouver, Canada, 2000, p17[6] Lorento D.P. unpublished paper
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 13
Instantaneous Heat Flux AssumedInstantaneous Heat Flux Assumed
0
1
2
3
4
5
0 10 20 30 40 50 60
Heat Flux (MW/m2)
Time Below Meniscus (sec.)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 14
Parametric StudyParametric Study
Assume:– Unique heat flux profile down mold– Ideal mold operation to achieve uniform heat flux
around mold parameters– Ideal spray zone managed to produce no change in
surface temperature below mold exitVary:– Casting speed for given section size and mold length
until failure criterion is just exceeded
Assume:– Unique heat flux profile down mold– Ideal mold operation to achieve uniform heat flux
around mold parameters– Ideal spray zone managed to produce no change in
surface temperature below mold exitVary:– Casting speed for given section size and mold length
until failure criterion is just exceeded
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 15
Conditions of Parametric StudyConditions of Parametric Study
7381(s120), 10797(s175), 15433(s250)Node Number7200(s120) ,10560(s175) ,15120(s250)Element Number
1459.9090% Solid Temperature (oC) (Damage strain accumulation begins)
1477.0270% Solid Temperature (oC) (Shell Thickness)
1500.72Liquidus Temperature (oC)1411.79Solidus Temperature (oC)1540.0Pouring Temperature (oC)0.001 ~ 0.5Time Step (sec.)
0.1x1.0 (at surface), 1.4x1.0 (at center)Mesh Size (mm x mm)0.3Time of Turning on Ferrostatic Pressure (sec.)0.75 (on both faces)Taper (%/m)600, 800, 1100Total Mold Length (mm)500, 700, 1000Working Mold Length (mm)120x120, 175x175, 250x250Billet Section Size (mm x mm)0.27C, 1.52Mn, 0.34Si, 0.015S, 0.012PMaterial Composition (wt%)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 16
Surface Temperature History Surface Temperature History
DISTANCE-BELOW-MENISCUS(mm)
TEM
PER
ATU
RE(
C)
0 250 500 750 1000600
700
800
900
1000
1100
1200
1300
1400
1500
TEMPERATURE(C) - Horizontal Face CenterTEMPERATURE(C) - Vertical Face CenterTEMPERATURE(C) - Corner
5.0Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
DISTANCE-BELOW-MENISCUS(mm)TE
MPE
RAT
UR
E(C
)0 250 500 750 1000600
700
800
900
1000
1100
1200
1300
1400
1500
TEMPERATURE(C) - Horizontal Face CenterTEMPERATURE(C) - Vertical Face CenterTEMPERATURE(C) - Corner
Mold Exit
2.2Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 17
Shell Thickness HistoryShell Thickness History
DISTANCE-BELOW-MENISCUS(mm)SH
ELL-
THIC
KNES
S(m
m)
0 100 200 300 400 500 600 7000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
SHELL-THICKNESS(mm) - CenterSHELL-THICKNESS(mm) - Corner
DISTANCE-BELOW-MENISCUS(mm)
SHEL
L-TH
ICKN
ESS(
mm
)
0 100 200 300 400 500 600 7000
5
10
15
SHELL-THICKNESS(mm) - CenterSHELL-THICKNESS(mm) - Corner
5.0Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
2.2Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 18
Surface Temperature Profile(Mold Exit and Below)
Surface Temperature Profile(Mold Exit and Below)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.2Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
X(mm), Y(mm)
TEM
PER
ATU
RE(
C)
0 10 20 30 40 50 60600
700
800
900
1000
1100
1200
TEMPERATURE(C) - Horizontal FaceTEMPERATURE(C) - Vertical Face
Y(mm), X(mm)TE
MPE
RAT
UR
E(C
)0 10 20 30 40 50 60600
700
800
900
1000
1100
1200
TEMPERATURE(C) - Horizontal FaceTEMPERATURE(C) - Vertical Face
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.0Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 19
Temperature Contour and Distorted Shape(Mold Exit)
Temperature Contour and Distorted Shape(Mold Exit)
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TEMPERATURE(C)1500.721477.021411.7913501300125012001150110010501000950900
11.16 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 TEMPERATURE(C)1500.721477.021411.7913501300125012001150110010501000950900
8.10mm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 20
Temperature Contour and Distorted Shape(200 mm Below Mold Exit)
Temperature Contour and Distorted Shape(200 mm Below Mold Exit)
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TEMPERATURE(C)1500.721477.021411.7913501300125012001150110010501000950900
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
X(mm)Y(
mm
)
0 10 20 30 40 50 60
0
10
20
30
40
50
60 TEMPERATURE(C)1500.721477.021411.7913501300125012001150110010501000950900
8.10mm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 21
Bulging Shapes(Mold Exit and 200 mm Below Mold Exit
Bulging Shapes(Mold Exit and 200 mm Below Mold Exit
Y(mm), X(mm)
Dis
plac
emen
t(m
m)
0 10 20 30 40 50 60
0.3
0.4
0.5
0.6
U-DISPLACEMENT(mm) - Mold ExitV-DISPLACEMENT(mm) - Mold ExitU-DISPLACEMENT(mm) - 200mm below Mold ExitV-DISPLACEMENT(mm) - 200mm below Mold Exit
Y(mm), X(mm)D
ISPL
ACEM
ENTS
(mm
)0 10 20 30 40 50 60-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
U-DISPLACEMENT(mm)V-DISPLACEMENT(mm)
5.0Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
2.2Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 22
ObservationsObservations
Surface temperature is higher for the higher casting speed cases due to their shorter dwell time in the mold.Surface temperature at the center of the face is higher than that at the corner due to 2D heat extraction at corner.Shell thickness at the mold exit is thinner as the casting speed increasing.The amount of bulging increases as the casting speed increasing. Billet surface shrinks for the 2.20 m/min casting speed case, while bulges around 3 mm for the 5.0 m/min casting speed case.
Surface temperature is higher for the higher casting speed cases due to their shorter dwell time in the mold.Surface temperature at the center of the face is higher than that at the corner due to 2D heat extraction at corner.Shell thickness at the mold exit is thinner as the casting speed increasing.The amount of bulging increases as the casting speed increasing. Billet surface shrinks for the 2.20 m/min casting speed case, while bulges around 3 mm for the 5.0 m/min casting speed case.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 23
Total Strains X(At Mold Exit)
Total Strains X(At Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-X(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-X(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
11.20 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 24
Total Strains X(200 mm Below Mold Exit)
Total Strains X(200 mm Below Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 60
0
10
20
30
40
50
60 TOTAL-STRAIN-X(%)21.510.80.60.40.20
-0.2-0.6-0.8-1-1.5-2
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-X(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 25
Total Strains Y(At Mold Exit)
Total Strains Y(At Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-Y(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-Y(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
11.20 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 26
Total Strains Y(200 mm Below Mold Exit)
Total Strains Y(200 mm Below Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 60
0
10
20
30
40
50
60 TOTAL-STRAIN-Y(%)21.510.80.60.40.20
-0.2-0.4-0.6-0.8-1-1.5-2
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 TOTAL-STRAIN-Y(%)10.80.60.40.20
-0.2-0.4-0.6-0.8-1
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 27
Strain History Crack sensitive off-corner subsurface location
Strain History Crack sensitive off-corner subsurface location
DISTANCE-BELOW-MENISCUS(mm)ST
RAI
NS
(%)
TEM
PER
ATU
RE(
C)
0 1000 2000 3000 4000-2
-1
0
1
2
3
4
5
6
7
8
9
10
1400
1450
1500
1550
TOTAL-STRAIN-X(%)PLASTIC-STRAIN-X(%)THERMAL-STRAIN(%)ELASTIC-STRAIN-X(%)FLOW-STRAIN-X(%)TEMPERATURE(C)DAMAGE-CRITERIA3(%)
Brittle Temperature Range
DISTANCE-BELOW-MENISCUS(mm)
STR
AIN
S(%
)
TEM
PER
ATU
RE(
C)
0 500 1000 1500 2000-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
1400
1450
1500
1550
TOTAL-STRAIN-X(%)PLASTIC-STRAIN-X(%)THERMAL-STRAIN(%)ELASTIC-STRAIN-X(%)FLOW-STRAIN-X(%)TEMPERATURE(C)DAMAGE-CRITERIA3(%)
Brittle Temperature Range
(6.7,17.4)Location (x mm, y mm)
5.0Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
(6.7,17.4)Location (x mm, y mm)
2.2Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 28
ObservationsObservationsStrains in X and Y directions are mirror imagesThere is little plastic strain developed for the normal casting speed case at the off-corner subsurface location, while substantial amount of plastic strain is built up at the off-corner subsurface location for the high casting speed.High tensile total strain in liquid indicates stretching of the liquid domain by ferro-static pressure, which causes fluid flow filling (ie. “flow strain”).High tensile strain region below mold exit near solidifying front in direction across dendrites is a dangerous location for causing off-corner hot tear cracks.
Strains in X and Y directions are mirror imagesThere is little plastic strain developed for the normal casting speed case at the off-corner subsurface location, while substantial amount of plastic strain is built up at the off-corner subsurface location for the high casting speed.High tensile total strain in liquid indicates stretching of the liquid domain by ferro-static pressure, which causes fluid flow filling (ie. “flow strain”).High tensile strain region below mold exit near solidifying front in direction across dendrites is a dangerous location for causing off-corner hot tear cracks.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 29
Hot Tear Fracture Criterion(Young Mok WON**)
Hot Tear Fracture Criterion(Young Mok WON**)
CTsteelCfornm
fTfTTwhere
T
thresholdDamage
oB
ssB
nB
mc
c
9%27.002821.0,8638.0*,3131.0*)99.0()9.0(
:
,
**
=∆===
=−==∆
∆=
ϕ
εϕε
ε
&
** Critical fracture strain is calculated based on the empirical equation above by Y.M. WON et. al. which is published in Met. Trans. B, Vol. 31B, August, 2000.
cflowinelastic εεε >+Σ )( when occurs Fracture :CriterionCrack Solid 99%Solid 90%
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 30
Failure Criterion Evaluation: Failed Points(V = 5.0 m/min)
Failure Criterion Evaluation: Failed Points(V = 5.0 m/min)
0.00700.02646.2160.0073490.00630.007015.496.5830800.00600.007616.706.9830200.00510.014017.586.9829590.00640.009319.936.5927750.00740.011119.656.2127740.00780.009020.556.2127130.00680.009221.726.5926530.00770.012121.456.2126520.00710.014959.105.85890.00910.018160.005.85280.00660.021560.005.5027Damage Threshold Damage Strain YY (mm)X (mm)Node No.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 31
Damage Strain X(At Mold Exit)
Damage Strain X(At Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA3(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60DAMAGE-CRITERIA3(%)
0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
11.20 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 32
Damage Strain X(200 mm Below Mold Exit)Damage Strain X(200 mm Below Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 60
0
10
20
30
40
50
60DAMAGE-CRITERIA3(%)
0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA3(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 33
Damage Criterion Y(At Mold Exit)
Damage Criterion Y(At Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA1(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60DAMAGE-CRITERIA1(%)
0.10.080.060.040.020
-0.02-0.04-0.06-0.1
11.20 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 34
Damage Criterion Y(200 mm Below Mold Exit)
Damage Criterion Y(200 mm Below Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 60
0
10
20
30
40
50
60DAMAGE-CRITERIA1(%)
0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA1(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 35
Bulging Histories and Effect of Casting SpeedBulging Histories and
Effect of Casting Speed
700Working Mold Length (mm)
120x120Section Size (mm x mm)
DISTANCE-BELOW-MENISCUS(mm)
DIS
PLAC
EMEN
TS(m
m)
0 1000 2000 3000 4000 5000 6000
-40
-35
-30
-25
-20
-15
-10
-5
0
U-DISPLACEMENT(mm)V-DISPLACEMENT(mm)
Vc = 2.2m/min Vc = 4.6m/min
Vc = 4.8m/min
Vc = 5.0m/min
Vc = 6.0m/min
Vc = 10.0m/min
0
10
20
30
40
50
2 3 4 5 6 7 8 9 10
Maximum Bulging V (mm)Maximum Bulging U (mm)
Casting Speed (m/min)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 36
Maximum Bulging vs Casting Speed(Working Mold Length: 500 mm)
Maximum Bulging vs Casting Speed(Working Mold Length: 500 mm)
0
20
40
60
80
100
120
2 3 4 5 6 7
Maximum Bulging vs. Casting Speed(Section = 175x175mm, Working Mold Length = 500mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
0
5
10
15
20
2 3 4 5 6 7 8 9
Maximum Bulging vs. Casting Speed(Section = 120x120mm, Working Mold Length = 500mm)
Maximum Bulging V (mm)Maximum Bulging U (mm)
Casting Speed (m/min)
0
2
4
6
8
10
12
14
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Maximum Bulging vs. Casting Speed(Section = 250x250mm, Working Mold Length = 500mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 37
Maximum Bulging vs Casting Speed(Working Mold Length: 700 mm)
Maximum Bulging vs Casting Speed(Working Mold Length: 700 mm)
0
10
20
30
40
50
60
70
80
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Maximum Bulging vs. Casting Speed(Section = 250x250mm, Working Mold Length = 700mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
0
10
20
30
40
50
2 3 4 5 6 7 8 9 10
Maximum Bulging vs. Casting Speed(Section = 120x120mm, Working Mold Length = 700mm)
Maximum Bulging V (mm)Maximum Bulging U (mm)
Casting Speed (m/min)
0
1
2
3
4
5
6
7
2 2.5 3 3.5 4 4.5
Maximum Bulging vs. Casting Speed(Section = 175x175mm, Working Mold Length = 700mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 38
Maximum Bulging vs Casting Speed(Working Mold Length: 1000 mm)
Maximum Bulging vs Casting Speed(Working Mold Length: 1000 mm)
0
10
20
30
40
50
60
70
80
0.5 1 1.5 2 2.5 3 3.5 4 4.5
Maximum Bulging vs. Casting Speed(Section = 250x250mm, Working Mold Length = 1000mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
0
5
10
15
20
25
30
35
40
2 2.5 3 3.5 4 4.5
Maximum Bulging vs. Casting Speed(Section = 175x175mm, Working Mold Length = 1000mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
0
2
4
6
8
10
12
2 3 4 5 6 7 8 9 10
Maximum Bulging vs. Casting Speed(Section = 120x120mm, Working Mold Length = 1000mm)
Maximum Bulging U (mm)Maximum Bulging V (mm)
Casting Speed (m/min)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 39
Critical Casting SpeedCritical Casting Speed
1
2
3
4
5
6
7
100 120 140 160 180 200 220 240 260
(WML = 500mm)(WML = 700mm)(WML = 1000mm)
Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 40
Stress Z(At Mold Exit)Stress Z
(At Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 STRESS-Z(MPa)1086420
-2-4-6-8-10
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 STRESS-Z(MPa)1086420
-2-4-6-8-10
11.20 mm
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 41
Stress Z(200 mm Below Mold Exit)
Stress Z(200 mm Below Mold Exit)
X(mm)Y(
mm
)0 10 20 30 40 50 60
0
10
20
30
40
50
60 STRESS-Z(MPa)1086420
-2-4-6-8-10
8.10mm
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 STRESS-Z(MPa)1086420
-2-4-6-8-10
13.81 mm
900Distance below Meniscus (mm)
10.80Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
900Distance below Meniscus (mm)
24.60Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 42
Damage Strain Z(At Mold Exit)
Damage Strain Z(At Mold Exit)
X(mm)
Y(m
m)
0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA2(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
X(mm)Y(
mm
)0 10 20 30 40 50 600
10
20
30
40
50
60 DAMAGE-CRITERIA2(%)0.10.080.060.040.020
-0.02-0.04-0.06-0.08-0.1
700Distance below Meniscus (mm)
8.40Time from Meniscus (sec.)
5.00Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
700Distance below Meniscus (mm)
19.10Time from Meniscus (sec.)
2.20Casting Speed (m/min)
700Working Mold Length (mm)
120x120Section Size (mm x mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 43
ConclusionsConclusions
Parametric study was performed to investigate the maximum casting speed for different square sections sizes and mold lengths with uniform heat flux around the mold parameters.Excessive bulging below mold exit may generate subsurface of corner longitudinal cracks due to hinging.Bulging criterion (4~10 mm maximum) and the hot tearing damage criterion indicate the same critical casting speed due to sub-mold bulging for certain section size and mold length.Excessive tensile stresses built up at the billet corner within the mold may generate transverse corner cracks due to high corner cooling.
Parametric study was performed to investigate the maximum casting speed for different square sections sizes and mold lengths with uniform heat flux around the mold parameters.Excessive bulging below mold exit may generate subsurface of corner longitudinal cracks due to hinging.Bulging criterion (4~10 mm maximum) and the hot tearing damage criterion indicate the same critical casting speed due to sub-mold bulging for certain section size and mold length.Excessive tensile stresses built up at the billet corner within the mold may generate transverse corner cracks due to high corner cooling.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Chunsheng Li • 44
Future WorkFuture Work
The influence of mold distortion, taper, imperfect contact between mold wall and billet surface, as well as sub-mold cooling pattern to the maximum casting speed will be investigated.
The influence of mold distortion, taper, imperfect contact between mold wall and billet surface, as well as sub-mold cooling pattern to the maximum casting speed will be investigated.