ANNUAL REPORT 2010ANNUAL REPORT 2010ccc.illinois.edu/s/2010_Presentations/14...University of...
Transcript of ANNUAL REPORT 2010ANNUAL REPORT 2010ccc.illinois.edu/s/2010_Presentations/14...University of...
ANNUAL REPORT 2010ANNUAL REPORT 2010UIUC, August 12, 2010
Stress and Hot Tearing of Solidifying
Steel Shells: Experiment andSteel Shells: Experiment and
Simulation
Matthew Rowan(Ph. D. Student)(Ph. D. Student)
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
Background
• Stress develops in solidifying shell due to: – 1) Thermal loading– 1) Thermal loading – 2) Mechanical loading
• Phenomena:– Thermal contraction– Phase transformation– Temperature gradientsTemperature gradients– Interface friction
• Leads to CracksBernhard C.:Anforderungen an prozessorientierte Heißrissbildungsmodelle BHM, Vol. 149 (2004), 90-95.
– Internal hot tears– Surface cracks
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • BG Thomas 2
Bernhard C.:Anforderungen an prozessorientierte Heißrissbildungsmodelle BHM, Vol. 149 (2004), 90-95.
Objectives
1) Develop a thermo-mechanical model of the Submerged Split Chill Contraction (SSCC) testSubmerged Split Chill Contraction (SSCC) test
2) Predict temperature measurements, shell growth ) p ghistory and reaction forces
3) Combine experiments and models to enhance3) Combine experiments and models to enhance understanding of the mechanical behavior of steel during initial solidification and hot tearingduring initial solidification and hot tearing
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SSCC Experimental Apparatus
Data:Force Position
Fz such that∆z = 0
Force, Position, Temperature
Welded Steel
60
Fixed Part
Cross Section
Plate
Spray CoatedZrO2
(outer surface)
Thermocouples
Shell
Steel Melt
r
z
r
z
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Pierer R., Bernhard C., High Temperature Behavior during Solidification of Peritectic Steels under Continuous Casting Condiitions, Materials Science & Technology (MS&T '06), Conference and Exihibition, Cincinnati, USA, October 2006
Steel Melt
Hot Tear Formation in SSCC
Cylinder expands Shell tries
Liqu id
to contract
Liqu id Stee l Cylinder prevents
contraction of solidifying shelly g
S olid ify ingS he ll
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Hot Tear Formation in SSCC
Tensile StrainStrain
Tensile strains develop perpendicular to dendrite
growth directiong
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Hot Tear Formation in SSCC
Tensile StrainStrain
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Pierer R., Michelic S., Bernhard C. A Hot Tearing Criterion for the Continuous Casting Process, Private Communication.
Hot Tear Formation in SSCC
Tensile StrainStrain
Bernhard C.:Anforderungen an prozessorientierte Heißrissbildungsmodelle BHM, Vol. 149 (2004), 90-95
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SSCC Test
Final Shell ShapeFinal Shell Shape
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Removed Solidified Shell
Half 1 Half 2Half 1 Half 2
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Experimental Data
• Experiments performed at University of Leoben
• Thermocouple measurements– 2 locations in the test cylindery
– 2 locations in the steel melt
• Contraction Force• Contraction Force
• Shell Thickness
• Alloying effect important– C, Si, Mn, P, S, Ni
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, , , , ,
Thermo-mechanical Modeling
• Solve 2-D axisymmetric transient heat conduction and elastic-viscoplastic stress equationand elastic-viscoplastic stress equation
• Temperature and phase-dependent – thermal conductivity
– specific heat
coefficient of thermal e pansion– coefficient of thermal expansion
– elastic modulus
• Implement Kozlowski III and modified power law constitutive relations into ABAQUS using Koric UMAT routine* * Koric S Thomas B G “Efficient thermo mechanical model for solidification
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* Koric, S, Thomas, B. G., Efficient thermo-mechanical model for solidification processes”, International Journal for Numerical Methods in Engineering, Vol. 66 (12), 2006, pp. 1955-1989.
Phase Fraction – PP05 Case
%C %Mn %S %P %Si %Al %Fe
0.315 1.44 0.0051 0.0039 0.356 0.0715 Balance
Phase Fraction History
0 91
0.315 1.44 0.0051 0.0039 0.356 0.0715 Balance
0 60.70.8
0.9
tion Austenite
From CON1D:Tliquidus = 1511.3 oCT lid = 1462 6 oC
0.30.4
0.50.6
Phas
e Fr
act
Delta
Liquid
Tsolidus 1462.6 CTδ→γ, begin = 1489.7 oC
00.1
0.20.3P
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1350 1400 1450 1500 1550Temperature, oC
Steel Property EquationsTemperature-dependent properties: k and Η [Pehlke,1982],
Ε [Mizukami,1977], αt [Pehlke,1982, Harste,1988 for solid, Cramb, 1993 for liquid].
Elastic-viscoplastic model for Austenite (Kozlowski)
( ) ( ) ( ) ( )( ) ( )( ) ( )( )( ) ( )( )
( )( ) ( )
32 1 4
1
3
1/ sec. % exp 4.465 10
130 5 5 128 10
oo
f T Kf T Ko o o
o o
f C MPa f T K K T K
f T K T K
ε σ ε ε −
−
= − − ×
= − ×
( )( ) ( )( )( ) ( )( )( ) ( )
( )
1
32
33
24 4 5
130.5 5.128 10
0.6289 1.114 10
8.132 1.54 10
(% ) 4.655 10 7.14 10 % 1.2 10 %
o o
o o
f T K T K
f T K T K
f T K T K
f C C C
−
−
= − ×
= − + ×
= − ×
= × + × + ×
Modified Power Law Model for δ-ferrite (Zhu)
( ) ( ) ( )( ) 5.52
1/ sec. 0.1 (% ) 300 (1 1000 )n
o mMPa f C T Kε σ ε−
= +
( ) ( )( )
( )
25.56 104
5
4
% 1.3678 10 %
9.4156 10 0.3495
1 1.617 10 0.06166
o
o
f C C
m T K
n T K
−− ×
−
−
= ×
= − × +
= × −
February 15-19, 2009, San Francisco, CA
Constitutive Behavior of Steel - Tension
δ+L
δδ+γ
γ Lines:
Constitutive Model10γ Constitutive Model
Predictions
Symbols:
W *
* P. J. Wray, Met. Trans, A, V7A, 1976, P1621-1627
1
ELEC FE - 2.3x10 -2 (s-1)
ELEC FE - 2.8x10-5 (s
-1)
FE 0.028%C - 2.3x10-2
(s-1)
FE 0.028%C - 2.8x10-5
(s-1)
FE 0.044%C - 2.3x10-2
(s-1)
Wray measurements*
m
FE 0.044%C - 2.8x10 -5 (s-1)
FE 3.0%Si - 2.3x10-2
(s-1)
FE 3.0%Si - 2.8x10-5
(s-1)
dε/dt 2.3x10-2 (s
-1)
dε/dt 2.8x10-5 (s
-1)
37m 3.2mm0.1
1200 1250 1300 1350 1400 1450 1500 1550
Temperature ( oC)
Model Implementation: If >10% delta-ferrite: delta-ferrite model (Zhu)
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Model Implementation: If >10% delta-ferrite: delta-ferrite model (Zhu)
If <10% delta-ferrite: austenite (Kozlowski)
Constitutive Behavior of Steel - Creep
*Kozlowski, P et al, “Simple Constitutive Equations for Steel at High Temperature”, Met Trans A Vol 23A 1992 pp 903 918
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Met. Trans. A, Vol. 23A, 1992, pp. 903-918.
Model Validation
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Image courtesy of L. Hibbeler
Comparison with Analytical Solution
J.H. Weiner and B.A. Boley, “Elasto-Plastic Thermal Stresses in a Solidifying Body.” Journal Courtesy of L. Hibbeler
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of the Mechanics and Physics of Solids, 11 (1963), No. 3. pg 145-154.
Boundary Conditions
Upper Part
Lower Part
C ti & R di ti
AUpper Part
Upper Part
Lower Part
C ti & R di ti
AUpper Part
A
Convection & Radiation
BZirconia
Lower PartAir
Gap
A
Convection & Radiation
BZirconia
Lower PartAir
Gap 4-node axisymmetric elements
Ti iti l t l lt ~1540 oC
ContainerSidewall
SteelMelt
Zirconia
B
ContainerSidewall
SteelMelt
Zirconia
B
Tinitial, steel melt 1540 C
Tinitial, test cylinder =25 oC
No Heat Flux
Zero Traction
z
A
Centerline
No Heat Flux
Zero Traction
zz
A
Centerline
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rContainer Bottom
rrContainer Bottom
Boundary Conditions - Interaction
z0, 0.040 m V t 0> ⋅ >V = -0 1 m/s z
z
z2
z
,
1850, 0.047 m V t 0.040 mW
HTC 2500, 0.088 m V t 0.047 mm K
1850, 0.110 m V t 0.088 m
≥ ⋅ ≥ = > ⋅ >
≥ ⋅ ≥Interface|begin
Vz = 0.1 m/s
z0, V t 0.110 ⋅ >
Steel – Steel Melt
The interface is treated in a Lagrangian
Zirconia – Steel Melt
The interface is treated in a Lagrangian frame of reference.
The conditions on the HTC determine the thermal interaction between the two
Interface|end Steel – Steel Melt
No Interaction
z
surfaces.
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r
Temperature History – PP05
z
r
Note short delay
in Tincrease (immersion).
TC TM
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z
Shell Growth ProfileShell Thickness Prediction
1416
mm
2468
1012
hell
Thi
ckne
ss, m
Simulation
Experiment
02
0 10 20 30
Simulation Time, sec
Sh
z
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r
Stress Perpendicular to Shell Growth Direction, 25 sec,
z
Stress is location
and time dependant.
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r
z
Phase Dependant Shell Strength
2
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
2
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
2
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
4
6
1450
1500
1550
re, o C
MP
a
L+γL+δ+γ
L+δL
-2
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
5 sec 15 sec-2
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
5 sec 15 sec-2
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
0
2
1350
1400
1450
Tem
per
atu
r
Z,Z
Str
ess,
ML+γ
γ
L+δ+γ
5 sec 15 sec
UP 1 Temperature, UP 1
-41300
0 2 4 6 8 10Distance from Test Body, mm
6
1500
1550
C
L+δ+γL+δL
-21300
0 2 4 6 8 10Distance from Test Body, mm
UP 1 Temperature, UP 1
-41300
0 2 4 6 8 10Distance from Test Body, mm
6
1500
1550
C
L+δ+γL+δL
-21300
0 2 4 6 8 10Distance from Test Body, mm
UP 1UP 1 Temperature, UP 1
-41300
0 2 4 6 8 10Distance from Test Body, mm
6
1500
1550
C
L+δ+γL+δL
-21300
0 2 4 6 8 10Distance from Test Body, mm
UP 2LP 1
LP 2
Temperature, UP 2
Temperature, LP 1
Temperature, LP 2
Stress, UP 10
2
4
1400
1450
1500
mp
erat
ure
, o C
Str
ess,
MP
a
L+γ
γ
UP 2LP 1
LP 2
Temperature, UP 2
Temperature, LP 1
Temperature, LP 2
Stress, UP 10
2
4
1400
1450
1500
mp
erat
ure
, o C
Str
ess,
MP
a
L+γ
γ
UP 2LP 1
LP 2
UP 2LP 1
LP 2
Temperature, UP 2
Temperature, LP 1
Temperature, LP 2
Stress, UP 10
2
4
1400
1450
1500
mp
erat
ure
, o C
Str
ess,
MP
a
L+γ
γ
Stress, UP 2
Stress, LP 1
Stress, LP 2
-2
0
1300
1350
0 2 4 6 8 10
Tem
Distance from Test Body, mm
Z,Z
25 sec
z
Stress, UP 2
Stress, LP 1
Stress, LP 2
-2
0
1300
1350
0 2 4 6 8 10
Tem
Distance from Test Body, mm
Z,Z
25 secStress, UP 2
Stress, LP 1
Stress, LP 2
-2
0
1300
1350
0 2 4 6 8 10
Tem
Distance from Test Body, mm
Z,Z
25 sec
z
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rr
Spatial and temporal variant temperature and stress profile.
Solidification Force
( )# nodes
Sol Force Reaction Force ( )i=1
Sol. Force= Reaction Forcei
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z This is a single value from a shell solidifyingat a complex 3D interface.
So How Is the Force Determined?Determined?
1
2At t 10 sec F 476 N
3
4
Location Lower Part Upper Part Zirconia Interface Shell Shell + Liquid Liquid Total1 476 -476 N/A N/A N/A N/A N/A 04 475.9997 -476.0019 N/A N/A N/A N/A N/A -0.00225 476.00 -476.63 N/A 1.28 0.00 0.12 0.00 0.777 476 111 53 N/A 8 05 498 16 85 79 15 04 3 41
At t = 10 sec, Fmeasure = - 476 N
56
7
7 476 111.53 N/A 8.05 -498.16 -85.79 -15.04 -3.418 476 -19.55 N/A 0 -442.35 1.35 -15.48 -0.039 -39825.81 N/A 40410.78 -3.42 -588.1 7.26 -10.28 -9.5711 -71768.13 N/A 72793.15 -2.3 -1017.47 3.11 -12.68 -4.3213 -7303.56 N/A 8416.86 3.12 -1102.38 3.52 -17.53 0.03
891011
Increasing shell force magnitude Force ≈ 0Large forces
1213
No Single Location Matches Measurement !
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Previous Methods of Determining Force
Previous Methodology: Slice taken at plane containing cylinder and melt thermocouple.gy p g y pThen constitutive model tailored to match experiments.
Current analysis indicates that this is an incorrect approach.
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Pierer R., Bernhard C. and Chimani C. Evaluation of Common Constitutive Equations for Solidifying Steel. BHM, 150, 2005, pp. 163-169.
Investigation of Interfacial Forces
F B d Di I t f• Free Body Diagram: Interface
• Force at Interface = Shear + Normal Forces
– In ABAQUS: CSHEARF2+CNORMF2Interface|begin
13
45
6
2
13
45
6
2
In ABAQUS: CSHEARF2 CNORMF2
• I will plot the running sum of these two forces at each node
E h l tt d l i th d l i6
7
8
6
7
8
– Each plotted value is the nodal + previous node values
98
10119
8
1011
z
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r
Comparison of Interface Forces and Shell Slicesand Shell Slices
-dir, N
erim
ent)
z-
13
42
13
42 UP 1 on
–E
xpe
56
7
56
7
UP 2LP 1
LP 2 (Sim
ula
ti
Looking for where plotted force = 0 (Simulation = Experiment)This indicates the location that the force is actually being measured.
Forces found from slices (UP1 UP2 LP1 & LP2) match the local total
98
10119
8
1011
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Forces found from slices (UP1, UP2, LP1 & LP2), match the local total interface force.
r
z
Comparison of Interface Forces and Shell Slicesand Shell Slices
-dir, N
erim
ent)
z-
15 sec
on
–E
xpe
13
42
13
42 UP 1
(Sim
ula
tio
56
7
56
7
UP 2LP 1
LP 2This corresponds to the shell connecting
the upper and lower parts.98
10119
8
1011
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z
Solidification Force is Determined by Shell Interface Temperaturep
13
42
13
42 UP 15
6
7
56
7
UP 2LP 1
LP 2Interfacial location where SSCC test is measuring
force also, coincidentally, corresponds to the region of the interface at the highest temperature.
98
10119
8
1011
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z
The SSCC Measures
13
42
13
42 UP 15
6
7
56
7
UP 2LP 1
LP 2 The SSCC test measures the strength of the
98
10119
8
1011
The SSCC test measures the strength of the shell at the highest interfacial temperature, which also connects the upper and lower
parts!!!!
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z
Good Comparison between Max. Strain Prediction and Observed Cracks
Z,Z Inelastic Strain [%]
SSCC, PP05, 25 [sec]
15 1 3 5
Hot tears form between 90% and 99% fraction solid.
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z
ConclusionsModel capable of predicting thermo-mechanical
behavior of solidifying steel for different carbonbehavior of solidifying steel for different carbon contents
Validated with measured temperature profiles
Elastic-viscoplastic constitutive model utilizing ast c scop ast c co st tut e ode ut gseparate austenite and delta-ferrite equations appears reasonableappea s easo ab e
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ConclusionsThe SSCC test measures the strength of the
shell at the highest interfacial temperatureshell at the highest interfacial temperature, which also connects the upper and lower partsparts.
Cracks are predicted in regions of high surface temperature where local strain concentration causes hot tears between dendrites perpendicular to the solidification direction
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Acknowledgments
Continuous Casting Consortium Members
g
(ABB, Arcelor-Mittal, Baosteel, Corus, LWB Refractories, Nucor Steel, Nippon Steel, Postech, Posco, ANSYS-Fluent)
National Center for Supercomputing p p gApplications (NCSA) at UIUC – “Tungsten” cluster
Christian Doppler Laboratory (Univ. Leoben)
L Hibb l S id K i
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Lance Hibbeler, Seid Koric