Solidification Stresses and Hot Tearing in Solidifying...
Transcript of Solidification Stresses and Hot Tearing in Solidifying...
ANNUAL REPORT 2008UIUC, August 6, 2008
Matthew Rowan (Ph.D. Student)
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
Solidification Stresses and Hot
Tearing in Solidifying Steel Shells
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Background
• Stress develops in solidifying shell in CC due to: – 1) Thermal loading – 2) Mechanical loading
• Phenomena:– Thermal contraction– Phase transformation– Temperature gradients– Interface friction
• Leads to Cracks– Internal hot tears– Surface cracks C. Bernhard and G. Xia, Ironmaking
and Steelmaking, 2006
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Steel Shrinkage Varies with Composition
Fe-C equilibrium phase diagram
MoCrSiNiMnCcp %1.0%04.0%1.0%04.0%04.0% ⋅−⋅−⋅−⋅+⋅+=
Cp wt.-%
T,
°Cδ
δ+L
γ γ+L
L
γδ +
1536
1495
1393
0,1 0,17 0,5
C. Bernhard, Univ. Leoben, 2002
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SSCT Experiment
INDUCTION FURNACE
STEEL MELT(20kg, CONTROLLED
SUPER HEAT)
TEST DUMMY
140
5637Dimensions in [mm]
C. Bernhard, Univ. Leoben, 2007
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SSCT Experiment Operation
60
Spray CoatedZr-Oxide
(0.4 +/- 0.02mm)
Isolation
Data Acquisition
LoadCell
TemperatureMeasurement
Thermal Contraction
C. Bernhard, Univ. Leoben, 2007
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Measurements from Each Experiment
• Alloy composition
• Pour temperature
• Temperature Histories (2 thermocouples)– Inside Cylinder (2mm from exterior face)
– Melt (16-20mm from exterior face)• Varies with each test
• Final Shell Thickness
• Force History (load cell)
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Objectives
1) Create thermal-mechanical model of temperature & stress-strain behavior of the steel solidification experiment (cylinder & shell)
2) Validate model with all measurements
3) Plot model stress / strain histories to better understand experiment
4) Evaluate crack criteria
- compare model predictions based on previous crack criteria with crack measurements (this work and previous)
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Solution Procedure
• Thermal stress analysis model in ABAQUS– Temperature determines stress
– Employ user subroutines for constitutive equations and 2-level local integration method (Koric, 2006)
• Temperature, strain-rate, phase-, and C content dependant
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Model Assumptions
Assumptions:- axisymmetry
- no contact resistances at interface
- no heat transfer prior to t=0
- melt TC indicates time of start and end of test
- force data used in the event TC data failure
- no heat loss to container walls or top surface
- initial temp-gradient across Zr
- for stress convergence
- shell thickness defined at solid fraction = 0.1
- zero displacement of cylinder at immersion surface
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Model Validation – Analytical Solution
• Boley and Weiner
Twall = 1000 oC41.6
0.4Tinitial = 1495 oC
Units [mm]
oC1000Mold Temperature
oC1495Initial Temperature
GPa15Elastic Modulus above
Solidus Temp
GPa40Elastic Modulus at Mold
Temp.
kPa35Yield Stress above Solidus
Temp.
MPa20Yield Stress at Mold Temp.
--0.3Poisson’s Ratio
m/(moC)2.00E-05Coefficient of Expansion
W/(m-K)33Thermal Conductivity
kJ/kg272Latent Heat
J/(kg-K)661Specific Heat
kg/m37500Density
UnitsValueProperty
Tsol = 1494.38 oCTliq = 1494.48 oCTwall = 1000 oC, h = 220 kW/(m2-K)
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Temperature ValidationTemperature Profile Validation
1100
1150
1200
1250
1300
1350
1400
1450
1500
0 5 10 15 20 25
Time [sec]
Tem
per
atu
re [
oC
]
B&W 5mm
ABAQUS 5mm
B&W 10 mm
ABAQUS 10 mm
B&W 30mm
ABAQUS 30mm
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Stress Validation
Stress through the Plate Thickness
-20
-15
-10
-5
0
5
10
15
0 4 8 12 16 20
Distance Beneath Shell Surface (mm)
Str
ess
(MP
a)
Numerical 1s Analytical 1s2s 2s5s 5s10s 10s20s 20s30s 30s
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Shell Growth Validation
Shell Thickness Growth
02
46
810
1214
1618
20
0 5 10 15 20 25 30
Time (s)
Sh
ell
Th
ickn
ess (m
m)
Analytical Solution
Numerical Solution
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Verification – Tension Test
• Data based on experiments by Wray (1976)
• Abaqus with UMAT (Koric)
• Temperatures – 950 oC, 1100 oC
• Strain Rate – 1.4 x 10-4 [1/sec]
u (t)
36.8
3.2
( ) tL εtu 0=
Dimensions in [mm]
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Constitutive Equations for Solid Steel
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950 oC, 1.2 x 10-4 1/s
Plastic strain
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Str
ess,
MP
a
0
5
10
15
20
25
0.005% C - numerical0.005% C - experimental0.46% C - numerical0.46% C - experimental1.24% C - numerical1.24% C - experimental
Tensile Test Simulation
1100 oC, 1.2 x 10-4 1/s
Plastic Strain
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Str
ess
, M
Pa
0
2
4
6
8
10
12
14
0.005% C - numerical 0.005% C - experimental0.46% C - numerical0.46% C - experimental1.24% C - numerical1.24% C - experimental
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Provided Data• Alloying content
– C, Si, Mn, P, S, Ni• Combined to form ‘Cp’
– Crack formation sensitive to this factor
• Temperature– 2 locations in the test cylinder
• 2mm from molten steel interface
– 2 locations in the steel melt• Test dependent
– 16-20 mm from test cylinder
• Shell Thickness
• Force
Image Source:http://www.xnqy.cn/shebei1-e.htm
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SSCT Model Domain
C. Bernhard, Univ. Leoben, 2007
60
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2D Domain of Experimental Apparatus
No flux boundary conditions
No axial (y) displacement at top face of the cylinder
Axisymmetric elements (4 nodes)
Tinitial, steel melt ~1540 oC (1535-1548)Tinitial, test cylinder =25 oC
Mesh size biased to regionsof solidification and large temperature gradients
0.04mm plasma-sprayed zirconia layer at test cylinder and melt interface
Steel MeltTest Cylinder
Air Gap
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Experimental Steel - Composition
Steel No. C Si Mn P S Ni Cp
1 0.05 0.29 1.52 0.012 0.004 0.017 0.072 0.07 0.27 1.51 0.012 0.004 0.017 0.093 0.09 0.29 1.55 0.011 0.008 0.026 0.124 0.13 0.31 1.57 0.014 0.004 0.017 0.155 0.15 0.28 1.56 0.014 0.005 0.018 0.176 0.20 0.27 1.75 0.014 0.005 0.020 0.23
• Alloying content in terms of percentages
Data Source: University of Leoben
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Background – Experimental Conditions
19.8*
18.7*
20.3
24.6
19.6
24.7
Immersion Time*[sec]
15451508.7, 1454
8.750.236
15351513.5, 1467.8
8.90.175
15431514.8, 1470.2
10.140.154
15481518.1, 1476.3
8.50.123
15371520.1, 1486.6
8.760.092
15471521.5, 1494
8.80.071
Temperature (Pour, Liquidus, Solidus) [oC]
Shell Thickness
[mm]CpTest #
*(Derived from Melt TC, except tests 5&6 used estimated finish time)
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Temperature and Force Profile (Raw Data), Steel Test 3
0
500
1000
1500
2000
2500
3000
3500
4000
0 10 20 30
Raw Time Data [sec]
Fo
rce
[N]
0
200
400
600
800
1000
1200
1400
1600
Tem
per
atu
re [
oC
]
Force
Temperature
Sharp increase indicates immersion
t ~ 8.1 sec
Removal initiates t ~ 32.7 sec
Total simulation time
0 24.6Simulation time (s)-8.1
Sample Data File
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Data and Simulation Comparison
• Temperature history– Immersion (raw data, t ≠ 0) indicates time at which
simulation begins (simulation time, t = 0)
• Test completed when:– 1) Melt thermocouple temperature decreases
– 2) Force data decreases (indicated by those running the experiment)
• Neglect transient effect of immersing and extracting – ~2.5 seconds for immersion
– ~2.5 seconds for extraction
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Simulation Initiation
Temperature in the Steel Melt, 16 mm, Steel Test 3
0
200
400
600
800
1000
1200
1400
1600
1800
-10 -5 0 5 10 15 20 25 30
Simulation Time [sec]
Te
mp
era
ture
[oC
]
TM1
Simulation
tsimulation = 0 sectraw data = 8.1 sec
Simulation starts when temperature sharply increases
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Temperature Inside Test Cylinder, Test 3
0
100
200
300
400
500
600
700
-10 -5 0 5 10 15 20 25 30
Simulation Time [sec]
Te
mp
era
ture
[oC
]
TC1
TC2
Simulation
Temperature in the Steel Melt, 16 mm, Steel Test 3
0
200
400
600
800
1000
1200
1400
1600
1800
-10 -5 0 5 10 15 20 25 30
Simulation Time [sec]
Te
mp
era
ture
[oC
]TM1
Simulation
Temperature Histories
60
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Shell Thickness
Thickness measured on same planewhere thermocouples are located
Determined from temperature profilefs=0.1
TCB TCM
8.75
8.9
10.14
8.5
8.76
8.8
Shell Thickness [mm](Experimental)
8.06*6
7.1*5
8.84
8.83
9.12
8.561
Shell Thickness [mm](Simulation)
Test #
Steel 3, 24.6s
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Shell Growth Profile, Steel 3
Shell Thickness Growth, Steel 3
0123456789
10
0 5 10 15 20 25 30
SimulationTime [sec]
Sh
ell
Th
ick
ne
ss
[m
m]
Simulation, fs=0.1
Measurement
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Force Determination – Shell
shellydAσF ∫= ∑ ∫=elements
R
Riy,
i outer,
i inner,
rdr2πF σ
( )∑ −=elements
2i inner,
2i outer,iy, RRπσF
Test Cylinder
r
Ring of elements extending through shell
SolidifyingShell
θ
Router, i
Rinner, i
A - A
A A
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Axial Stress Distribution in Shell (Steel 3, t= 24.6 sec)
Note: Previous researchersonly look at one location
Delta Ferrite(1518.1 T > 1463 oC)
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Shell Strength
• Different phases present across the shell thickness
• Increase in strength occurs during phase transformation of delta ferrite to austenite
• Location of maximum force in shell may change during solidification– Multiple locations investigated
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Phase Fraction for 0.09% C Plain Carbon Steel
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
600 800 1000 1200 1400 1600
Temperature [oC]
Phas
e Fr
actio
n
Alpha
Gamma Austenite
Delta Ferrite
Liquid
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Axial Stress Distribution in Shell (Steel 3, t= 24.6 sec)
1
8Location of Maximum Strength
Changes During Simulation
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Austenite Formation (Red)5 seconds
10 seconds
24.6 seconds
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Phases Across Shell Thickness
T emperature and Stress Profile T hrough the Shell, Steel 3T ime = 10 sec
0
1
2
3
4
5
6
0.026 0.028 0.029 0.030 0.031 0.033 0.034 0.035
Distance from Center of Cylinder [m]
Str
es
s [
MP
a]
1300
1350
1400
1450
1500
1550
Te
mp
era
ture
[oC
]
Stress
Temperature
LL+δ
L+δ+γ
δ+γ
δγ
Location 4
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Shell Strength, Steel 3
Comparison of Shell Strengths vs. Location
0
500
1000
1500
2000
2500
-10 -5 0 5 10 15 20 25 30 35
Time [sec]
Fo
rce
[N
]
Experiment
1
2
3
4
5
6
7
8
Comparison of Experimental and Maximum Shell Strength
0
500
1000
1500
2000
2500
-10 -5 0 5 10 15 20 25 30 35
Time [sec]
Fo
rce
[N]
Experiment
Maximum Force
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Shell Strength Analysis
• Maximum shell strength depends on:– Heat transfer
– Temperature
– Formation of austenite
• Thickest shell section is not the strongest
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Hot Tearing Mechanisms
#) P.-D. Grasso, J.-M. Drezet and M. Rappaz, January 2002 JOM-e: http://www.tms.org/pubs/journals/JOM/0201/Grasso/Grasso-0201.html
Breaking of solid-solid bridges (Verö, 1936)Liquid film rupture (Pellini, 1952)Liquid distribution between dendrites/grains (Borland 1960)
Still basis of most hot tearing criteria
Segregation is important to hot tearing in steel (Bernhard, Pierer, 2007)Modeling of HTS in CC process as segregation phenomenon
#)
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Hot Tear Crack Prediction
• Simulations do not take cracking into account– Cracking indicated by ‘plateau’ in force measurement
data
• Time when simulation starts to deviate from experimental forces likely indicates start of crack formation
• To predict cracks: compare calculated and critical strain
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Calculation of Critical Strain
• Equation fit over large range of strain rates and cooling rates– (5 – 90 x 10-4 1/sec)
• ΔTB = Brittle temperature difference– Temperature difference between 90% and 99% solid
fraction
• Strain rate found from simulation* Won, MY, Yeo, TJ, Seol, DJ and Oh, KH, “A New Criterion for Internal Crack Formation in Continuously Cast Steels”, Met. Trans. B, Vol. 31B, 2000, pp. 779-94
0.3131 0.8638
0.02821crit
BTε
ε=
Δ*
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Inelastic Strain at Failure, t = 10 sec, Steel 3
12.2 % strain
6.2 % strain
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Summary of Critical Strain Results
2.99.4x10-4121470.161514.84
3.96.4x10-4101467.841513.475
2.68.7x10-4141476.261518.083
3.98.6x10-491493.991521.51
εcritε. (1/sec)ΔTbrittle
(oC)Tsol (oC)Tliq (oC)Steel #
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Critical Strain as a Function of Carbon Content
0
1
2
3
4
5
6
7
0 0.05 0.1 0.15 0.2 0.25
Carbon Content (% C)
Cri
tica
l S
trai
n (
%)
Simulation, Won Eqn.Simulation, ABAQUSMatsumiya, 1986
Critical Strain as a Function of Carbon Content
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Critical Strain Discussion
• Brittle Temperature Range – Determined from CON1D
• Inelastic Strains– High estimations
– Constitutive model formulation
– Enforcement of boundary condition
• Critical Strain– Better agreement with using Won formulation than
using ABAQUS values for strain
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Conclusions
• Model capable of predicting temperature profiles, shell thickness and forces and strains to failure for detailed case– Carbon content is an input variable
• Other steel cases:– Model needs improvement
• Inelastic strain over-predicts critical strain
– Empirical relation between critical strain and brittle temperature range
– CON1D differs with published data
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What We Need to Improve
• Need more certain values of experimental conditions– Pour Temperature (superheat )
• Shell thickness
– Experiment Duration
– Initial temperature of test cylinder• Time between tests?
– Multiple tests of one specific alloy to determine variance
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Acknowledgements
• Continuous Casting Consortium Members
• Christian Bernhard & Robert Pierer– University of Leoben
• National Center for Supercomputing Applications (NCSA) at UIUC
• ABAQUS
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Supplemental Material
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Linear Gradient Across Zirconia Layer
Comparison of Temperature Histories in Test Cylinder, Steel 3
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30
Simulation Time [sec]
Te
mp
era
ture
[oC
]
Linear Gradient
No Gradient