University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 1 Thermomechanical Behavior of the Solidifying Shell and Ideal Taper in a Funnel Mold CCC Annual Meeting 12 June 2007 Lance C. Hibbeler (MSME Candidate) University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 2 Acknowledgements • Continuous Casting Consortium Members (Nucor, Postech, LWB Refractories, Algoma, Corus, Labein, Mittal Riverdale, Baosteel, Steel Dynamics) • Begoña Santillana, Arnoud Kamperman, and Arie Hamoen (Corus RD&T, Corus Strip Products) • Dr. Seid Koric • National Science Foundation – DMI 05-28668 • National Center for Supercomputing Applications (NCSA) at UIUC • Dassault Simulia, Inc. (ABAQUS parent company)
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University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 1
Thermomechanical Behavior of the Solidifying Shell and Ideal Taper in a
Funnel Mold
CCC Annual Meeting
12 June 2007
Lance C. Hibbeler (MSME Candidate)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 2
• National Center for Supercomputing Applications (NCSA) at UIUC
• Dassault Simulia, Inc. (ABAQUS parent company)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 3
Outline
• Problem identification
• Simulation overview
• Model parameters
• Analysis procedures
• Model validation
• Discussion of results
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 4
Problem Identification
• Approximately 60% of breakouts on the Corus thin slab caster (IJmuiden, The Netherlands) over the past two years have been due to longitudinal face cracks – Mostly occurring in the transition region of the
funnel mold
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 5
Longitudinal Face Crack
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 6
Breakout from LFC
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 7
LFC Mechanisms
• The main mechanism of longitudinal face cracks is non-uniform heat transfer, caused by level fluctuations and/or by several mold phenomena
Shell buckling (excessive taper)
Necking (shell sliding, sticking)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 8
Funnel Mold Terminology
Inner Flat
Inner Curve
Outer Curve
Outer Flat
IF
IC
OC
OF
Top View
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 9
Mold Funnel Shapes
0
50
100
0 50 100 150 200 250 300 350 400 450 500
A-Configuration Mold
0
50
100
0 50 100 150 200 250 300 350 400 450 500
B-Configuration Mold
Axes show distance from cold face and distance from centerline in mm.
Thick line is top edge, thin line is bottom edge
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 10
LFC Locations
0
1
2
3
4
5
6
7
8
9
0 100 200 300 400 500 600 700
Distance from Center (mm)
Fre
qu
en
cy
(--
)
Inner Flat Inner Curve Outer Curve Outer Flat
January 2005 - January 2007
A-Configuration Molds
Data provided by A. Kamperman of Corus
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 11
Project Overview
• The purpose of this work is to use a numerical model to gain insight into the thermomechanical behavior of the solidifying steel shell in a thin-slab funnel mold
• One-way coupled thermomechanical model– Solve heat transfer problem
– Import results, then solve stress problem
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 12
Method of Analysis
• Finite element simulation with ABAQUS 6.6– Specializes in nonlinear problems
– Jobs easily scalable with multiple processors
– Robust contact algorithms
– Functionality extended through user subroutines
– Built-in pre-processing capabilities
– Customizable post-processing (with Python)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 13
Thermal Analysis
• Uses isotropic, temperature- and phase-dependent thermal properties– Thermal conductivity
– Specific heat capacity
• Constant density
• Analysis includes rate-of-change effects of temperature-dependent properties
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 14
Thermal Analysis
• Using simple heat flux profile– Numerical stability
• Fixed mesh of standard four-node heat transfer elements– Currently ~14k elements and ~15k nodes
• Implemented via default ABAQUS heat transfer routines
• Requires ~5 hours (2 CPUs)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 15
Mechanical Analysis
• Uses isotropic, temperature- and phase-dependent mechanical properties– Coefficient of thermal expansion
– Elastic modulus
• Constant density
• Uses Kozlowski III and modified power law constitutive models
• Liquid and mushy zone treated as very low elastic modulus, perfectly plastic solid
• Implemented via Koric’s UMAT subroutine
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 16
• Kozlowski III model for austenite [Kozlowski, 1991]
• Modified power law for delta-ferrite [Parkman, 2000]
Constitutive Equations
( ) ( ) ( ) ( )( ) ( )( ) ( )( )( ) ( )( )
( )( ) ( )( )( ) ( )( )( ) ( )
( )
32 1 4
1
31
32
33
24 4 5
1/ sec. % exp 4.465 10
130.5 5.128 10
0.6289 1.114 10
8.132 1.54 10
(% ) 4.655 10 7.14 10 % 1.2 10 %
oo
f T Kf T Ko o o
o o
o o
o o
f C MPa f T K K T K
f T K T K
f T K T K
f T K T K
f C C C
ε σ ε ε −
−
−
−
⎡ ⎤= − − ×⎢ ⎥⎣ ⎦
= − ×
= − + ×
= − ×
= × + × + ×
( ) ( ) ( )( )( ) ( )
( )( )
2
5.52
5.56 104
5
4
1/ sec. 0.1 (% ) 300 (1 1000 )
% 1.3678 10 %
9.4156 10 0.3495
1 1.617 10 0.06166
no m
o
o
MPa f C T K
f C C
m T K
n T K
ε σ ε−
−
− ×
−
−
= +
= ×
= − × +
= × −
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 17
Mechanical Contact
• Uses the ABAQUS surface-to-surface contact algorithm with a “softened” exponentialpressure-overclosure relationship– Mold is the master surface
– Steel shell is the slave surface (softer)
• Tangential friction factor* of µfrict = 0.16
• Uses a vector-based algorithm, so the curved surface of the funnel is easy to handle
* [Meng, Thomas, et. al., CMQ 45-1 p 79-94]
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 18
Mechanical Analysis
• Uses the exact same mesh as the thermal analysis, using the hybrid formulation (more stable in the liquid region) of four-node generalized plane strain elements
• Requires ~35 hours (2 CPUs)
• Working to optimize UMAT subroutine, though it is already many times faster than using the ABAQUS-native creep algorithm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 19
Finite-Element Mesh
CornerNear inside
of funnel
Domain discretization error ~0.05%
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 20
Dimensionality
• Full three-dimensional simulation is a very large and complicated task
• Domain can be two-dimensionalized by relating time to depth (x-y-z to x-y-t):
( )shell men cz t z v t= + ⋅
( ) ( )sin2osc
mold men c oscS
z t z v t tω= + ⋅ + ⋅
• Commonly called “traveling slice analysis”
• Simulated mold includes oscillation effects:2osc oscfω π= ⋅ ⋅
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 21
Traveling Slice – Half Speed
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 22
Dimensionality
• Some losses in simplifying from 3-D to 2-D– Out-of-plane bending
– Not a problem – investigating longitudinal cracks
What actual steel wants to do What the simulated steel does
[Koric, 2006]
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 23
Process Parameters
• Casting speed 5.5 m/min• Pour temperature 1545.0 ºC• Oscillation stroke 7.2 mm• Oscillation frequency 331 cycles/min• Strand width 1200 mm• Narrow face taper 1.0 %/m• Meniscus depth 104.2 mm• Time in mold 10.86 s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 24
Meniscus Depth
0
20
40
60
80
100
120
140
3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75
Casting Speed (m/min)
Dis
tan
ce
Be
low
Mo
ld T
op
(m
m)
Minimum = 90 mmMaximum = 125 mmAverage = 104.2 mmStd. Dev = 7.79 mm
Measurements from molds with 0-5 mm of wear
Data provided by A. Kamperman of Corus
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 25
Steel Properties
• Properties for Corus grade F12L from CON1D/CON2D models– Carbon content 0.045 %wt
– Solidus temperature 1507.51 ºC
– Liquidus temperature 1530.45 ºC
– Solidus/liquidus based on modified Clyne-Kurzsimple segregation model [Won and Thomas, 2001]
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 26
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 42
Realistic 1D Analysis
• Allow temperature-dependent properties and time-varying boundary conditions for a more realistic simulation, using a finer mesh than what could be used practically (at this point in time) in two dimensions– 300 x 1 row of elements over 30 x 0.1 mm domain
– Typical results away from funnel features
• Very fine mesh provides the ability to determine if an effect is a numerical error
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 43
Realistic 1D Results
1000
1100
1200
1300
1400
1500
1600
0 3 6 9 12 15
Distance Below Shell Surface (mm)
Te
mp
era
ture
(ºC
)
2.5s5s7.5s10.86s
γ
δ+γ
LL+δ
δ
-12
-9
-6
-3
0
3
6
0 3 6 9 12 15
Distance Below Shell Surface (mm)S
tre
ss
(M
Pa
)
2.5s5s7.5s10.86s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 44
Realistic 1D Results
-12
-9
-6
-3
0
3
6
0 2 4 6 8 10 12 14 16 18 20 22 24
Distance Below Shell Surface (mm)
Str
es
s (
MP
a)
10.86s
LL+δγ
δ+γ
δ
So
lidu
s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 45
Temperature Results
t = 10.8s (mold exit)
A-mold
B-mold
Parallel mold
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 46
Temperature Results
t = 10.8s
(mold exit)
Solidus
9.6 mm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 47
Temperature Results
t = 10.8s (mold exit)
A-mold
Slight two-dimensional heat transfer in funnel transition region
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 48
1000
1050
1100
1150
1200
1250
1300
0 50 100 150 200 250 300 350 400 450 500 550 600 650Distance from Center of Funnel (mm)
Te
mp
era
ture
(ºC
)
A-mold, 5s
Inner Flat Outer Curve Outer FlatInner Curve
Surface Temperature
Slight two-dimensional effects
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 49
Comparison of Temperature Variations Across Each Funnel
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 100 200 300 400 500 600 700 800 900 1000
Distance Below Meniscus (mm)
Ma
x A
bs
olu
te D
ev
iati
on
fro
m P
ara
llel
Mo
ld S
he
ll S
urf
ac
e T
em
pe
ratu
re (
ºC)
0 1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 11
Time in Mold (s)
A-mold B-mold
Wiggles are numerical effect
Effect grows with time, despite decreasing heat flux and increasing funnel radius
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 50
Funnel Stress Development
Tension
Compression
Compression
Tension
From Bending/Unbending
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 51
Funnel Shape DevelopmentFrom Change in Length
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0 100 200 300 400 500 600 700 800 900 1000
Distance Below Meniscus (mm)
Str
ain
(m
m/m
)
A-Mold B-Mold
Per
cent
cha
nge
in m
old
perim
eter
in
funn
el tr
ansi
tion
regi
on
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 52
Stress Transformation
• Unless otherwise noted, stress/strain results presented on graphs are transformed to a plane tangent to the funnel surface via:
( ) ( )cos 2 sin 22 2
x y x yx xy
σ σ σ σσ θ τ θ
+ −′ = + +
σx
σy
τxy
σx’
σy’
τx’y’
x’
xθ
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 53
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 55
Conclusions
• Larger funnel radii provides more uniform heat transfer in the funnel region
• The present antisymmetric funnel design concentrates strains in the funnel region
• Narrow face taper is equal in importance to funnel shape
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler 56
Upcoming Work
• Apply a more realistic, experimentally validated heat flux profile from CON1D [Santillana, Thomas, Hamoen, Hibbeler, Kamperman, van der Knoop, AISTech 2007]