thermo-mechanical behavior of the solidifying shell in a...
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ThermoThermo--Mechanical behavior of the Mechanical behavior of the solidifying shell in a beam blank and a thin solidifying shell in a beam blank and a thin
slab caster with a funnelslab caster with a funnel--moldmold
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 1
ANNUAL REPORT 2006Meeting date: June 16, 2006
Seid Koric Ph.D.Engineering Applications Analyst
National Center for Supercomputing Applications-NCSAUniversity of Illinois at Urbana-Champaign
ObjectivesTo predict the evolution of temperature, shape, stress and strain distribution in the solidifying shell in continuous casting mold by a nonlinear multipurpose commercial finite element package with an accurate approach.
Validate the model with available analytical solution and benchmarks with in-house code CON2D specializing in accurate modeling of 2D continuous casting.
To enable new model to be applied to the continuous casting problems by incorporating even more complete and realistic phenomena.
To perform a unique realistic 2D and 3D thermal stress analysis of solidification of the shell of a beam blank and thin slab caster that can accurately predict the mechanical state in some critical regions important to crack formation.
Apply FE results to find ideal taper, critical shell thickness, to predict damage strains and transverse and longitudinal cracks and more.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 3
Why ABAQUS ?
It has a good user interface, other modelers in this field can largely benefit from this work, including our final customers – the steel industry.
Abaqus has imbedded pre and post processing tools supporting import of the major CAD formats. All major general purpose pre-processing packages like Patran and I-DEAS support Abaqus.
Abaqus is using full Newton-Raphson scheme for solution of global nonlinear equilibrium equations and has its own contact algorithm.
Abaqus has a variety of continuum elements: Generalized 2D elements, linear and quadratic tetrahedral and brick 3D elements and more.
Abaqus has parallel implementation on High Performance Computing Platforms which can scale wall clock time significantly for large 2D and 3D problems.
Abaqus can link with external user subroutines (in Fortran and C) linked with the main code than can be coded to increase the functionality and the efficiency of the main Abaqus code.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 4
Basic PhenomenaBasic PhenomenaOnce in the mold, the molten steel freezes against water-cooled walls of a copper mold to form a solid shell.
Initial solidification occurs at the meniscus and is responsible for the surface quality of the final product. To lubricate the contact, oil or powder is added to the steel meniscus that flows into the gap between the mold and shell.
Thermal strains arise due to volume changes caused by temp changes and phase transformations.Inelastic Strains develop due to both strain-rate independent plasticity and time dependant creep.
At inner side of the strand shell the ferrostaticpressure linearly increasing with the height is present.
Mold distortion and mold taper (slant of mold walls to compensate for shell shrinkage) affects mold shape and interfacial gap size.
Many other phenomena are present due tocomplex interactions between thermal and mechanical stresses and micro structural effects. Some of them are still not fully understood.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 5
Governing EquationsHeat Equation:
Equilibrium Equation (small deformation assumption):
Rate Representation of Total Strain Decomposition:
Constitutive Law (Rate Form, No large rotations):
Inelastic (visco-plastic) Strain Rate (strain rate independent plasticity + creep):
Thermal Strain:
( )( ) ( )
H T T T Tk T k T
T t x x y yρ
⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞⎛ ⎞ ⎛ ⎞= + ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 6
( ) 0ox b∇ ⋅ σ + =
ie th:( )= − −Dσ ε ε ε 22 (k )
3= μ + − ⊗D I I I
thieel εεεε ++=
ie ie ie
2T, ,% ) :
3C= ε = ε εieε f( σ,
{ } ( ) ( )( ) [ ]Trefiirefth 000111TT)T(TT)T( −α−−α=ε
3 1' : ' , ' trace( )
2 3σ = = − σ Iσ σ σ σ
Computational Methods Used to Solve Governing Equations
Global Solution Methods (solving global FE equations)
-Full Newton-Raphson used by Abaqus
Local Integration Methods (on every material points integrating constitutive laws) [Thomas, Moitra, Zhu, Li, Koric, 1993-2006]
-Fully Implicit followed by local bounded NR
-Radial Return Method for Rate Independent Plasticity, for liquid/mushy zone only
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 7
Finite Elements Implementation-Heat EquationFE (weak) Form of Heat Equation:
Implicit Time Integration:
Time discretization of FE Form (nonlinear system of equations):
Incremental Solution by using Modified Newton-Raphson Scheme assuming
outside phase change range, and
where Hf is latent heat of fusion for
Temperature History is saved for a subsequent mechanical analysis.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 8
t
HHH
ttttt
Δ−
=Δ+
Δ+
[ ] ( ) [ ] [ ]q h
TT Tt t t T
o
V V S S
N1 TN H H dV k(T) dV N q dS [N] h(T T )dS 0
t+Δ ∂ ∂
ρ − + − − − =Δ ∂ ∂∫ ∫ ∫ ∫x x
[ ] [ ] [ ] [ ] [ ] [ ] { } [ ]
[ ] ( ) [ ]h q
h
t tTT T Tt t t t
i iiV V S S
T tTT t t t t t t
i o i
S V V
1 dHN N dV B k B dV N h N dS T N qdS
t dT
N1 T[N] h(T T )dS N H H dV k dV
t
+Δ+Δ +Δ
+Δ +Δ
⎡ ⎤⎛ ⎞ρ + − Δ = +⎢ ⎥⎜ ⎟Δ ⎝ ⎠⎢ ⎥⎣ ⎦
∂ ⎛ ⎞∂+ − − ρ − − ⎜ ⎟Δ ∂ ∂⎝ ⎠
∫ ∫ ∫ ∫
∫ ∫ ∫ x x
{ } { } { }t+Δt t+Δt t+Δti+1 i iT = T + ΔT
t tdH
cp(T)dT
+Δ⎛ ⎞ =⎜ ⎟⎝ ⎠
t tsol liqT T T+Δ< <
t t
liq sol
dH Hfcp(T)
dT T T
+Δ⎛ ⎞ = +⎜ ⎟ −⎝ ⎠
q h
T T T To
V V S S
T[N] HdV [N] k(t) dV [N] qdS [N] h(T T )dS
∂+ = + −
∂∫ ∫ ∫ ∫x
t tk
0,h h(T)T
+Δ∂⎛ ⎞ ≈ ≠⎜ ⎟∂⎝ ⎠
Finite Elements Implementation-Equilibrium Equation
Residual Force- Equilibrium imbalance between internal (stress) forces and externally applied loads due to material nonlinearity
Equilibrium is satisfied when Residual force vanishes.Incremental Solution of obtained by using Full Newton-Raphson Scheme:
Tangent Matrix [K] defined by means of Jacobian [J] (Consistent Tangent Operator)-consistent with local stress-update algorithm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 9
{ } [ ] { } [ ] { } [ ] { }T T T
V V S
R B dV N b dV N dAΦ
⎛ ⎞= σ − + Φ⎜ ⎟⎜ ⎟
⎝ ⎠∫ ∫ ∫
[ ]{ } { } { }tt1i
tttt1i
tt1i SPuK Δ+
−Δ+Δ+
−Δ+
− −=Δ
[ ] [ ][ ][ ]dVBJBKV
Ttt ∫=Δ+
t t
t tˆ
+Δ
+Δ
∂=∂Δσε
J
{ } { } { }t t t t t ti i 1 i 1u u u+Δ +Δ +Δ
− −= Δ +
{ }R({u}) 0=
Big Picture: : Materially Non-Linear FEM Solution Strategy in Abaqus with UMAT
University o f Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 10
IterationNR Global
[ ] [ ] { } { } { } { } 0i ; UU ; SS ; KK ttt0
ttt0
ttt0 ==== Δ+Δ+Δ+
1ii +=
[ ]{ } { } { }{ } { } { }-1i
tt-1i
tti
tt-1i
tt-1i
tt-1i
U U U
S - P U K
Δ+=
=ΔΔ+Δ+
Δ+Δ+Δ+
Tolerance
{ } { } { }ttti
tti U - U U Δ+Δ+ =Δ
t t t
Yes
Δ+=
IterationNR newStart No,
{ } { } { }⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦∑∫ ∫t+Δt T t+Δt T t+Δt
V A
P = N b dV + N Φ dA
ttat Vector Load External Global Δ+
{ } { } { } t t t
Equilibrium Configuration at t
U , S , P{ } Ttttt
tt
0} 0 0 1 1 {1 T )(T
database HT from T Nodal ReadΔ+Δ+Δ+
Δ+
=αε ttth
{ } [ ]{ }ttiU B
Increment StrainElement Δ+Δ+ Δ=Δ tt
iε
{ } { } { }tie
ttt , ,
Points Gauss allat
called UMAT
εεσ Δ+Δ
[ ] { }{ }∂
∂
t+Δt
t+Δt
Stress Update Algoritham
Implicit Integration of IVP
Calculation of CTO :
σJ =
Δε
{ } { } [ ]J , , ttie
tt Δ+Δ+ εσ
{ } { }
[ ][ ]
E
⎡ ⎤⎣ ⎦
⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
∫
∫
t+Δt T t+Δtel , i
Vel
t+Δt Tel, i Vel
lement Internal Force
and Element Tangent Matrix
S = B σ dV
K = B J B dV[ ] [ ] { } { }∑∑ Δ+Δ+Δ+Δ+ == tt
iel,tt
eltt
i el,tt
i S S , K K
Constitutive Models for Solid Steel (T<=Tsol)Unified (Plasticity + Creep) Approach
Kozlowski Model for Austenite (Kozlowski 1991)
Modified Power Law for Delta-Ferrite (Parkman 2000)
( ) ( ) ( ) ( )( ) ( )( ) ( )( )( ) ( )( )
( )( ) ( )( )( ) ( )( )( ) ( )
( )
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 −
−
−
−
⎡ ⎤= − − ×⎢ ⎥⎣ ⎦
= − ×
= − + ×
= − ×
= × + × + ×
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 11
( ) ( ) ( )( )( ) ( )
( )( )
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
−
−
− ×
−
−
= +
= ×
= − × +
= × −
1D Solidification Stress Problem for Program Validation
Analytical Solution exists (Weiner & Boley1963). Elastic in solid, Perfectly Plastic in liquid/mushy. No viscoplastic law for solid yet in this model.
Provides an extremely useful validation test for integration methods, since stress update algorithm in liquid/mushy zone is a major challenge !
Yield stress linearly drops with temp. from 20Mpa @ 1000C to 0.03Mpa @ Solidus Temp 1494.35C
A strip of 2D elements used as a 1D FE Domain for validation
Generalized plane strain both in y and z direction to give 3D stress/strain state
Tested both of our methods to emulate Elastic-Perfectly Plastic material behavior plus both Abaqus native CREEP integration methods.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 12
Constants Used in Abaqus Numerical Constants Used in Abaqus Numerical Solution of WB Analytical Test ProblemSolution of WB Analytical Test Problem
Conductivity [W/mK] 33.
Specific Heat [J/kg/K] 661.
Elastic Modulus in Solid [Gpa] 40.
Elastic Modulus in Liq. [Gpa] 14.
Thermal Linear Exp. [1/k] 2.E-5
Density [kg/m3] 7500.
Poisson’s Ratio 0.3
Liquidus Temp [O C] 1494.48
Solidus Temp [O C] 1494.38
Initial Temp [O C] 1495.
Latent Heat [J/kgK] 272000.
Number of Elements 300.
Uniform Element Length [mm] 0.1
Artificial and non-physical thermal BC from VB (slab surface quenched to 1000C),
replaced by a convective BC with h=220000 [W/m2K]
Simple calculation to get h, from surface energy balance at initial instant of time:
and for finite values)( ∞−=∂∂
− TThx
Tk 495
0001.0
49533 h=
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 13
Analytical, CON2D, and Abaqus Analytical, CON2D, and Abaqus Temperature and Stress ResultsTemperature and Stress Results
All different Stress Update Integration methods in Abaqus yield the same result, and are represented by a single Abaqus curve in bellow stress graph.
0 5 10 15 20 25 301000
1100
1200
1300
1400
1500
Distance to the chilled surface [mm]
Tem
pera
ture
[C
]
Analytical 5 secAbaqus 5 secCON2D 5 secAnalytical 21 secAbaqus 21 secCON2D 21 sec
0 5 10 15 20 25 30-25
-20
-15
-10
-5
0
5
10
15
Distance to the chilled surface [mm]
Str
ess
[MP
a]
Analytical 5 secAbaqus 5 secCON2D 5 secAnalytical 21 secAbaqus 21 secCON2D 21 sec
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 14
Modeling Features of 2D Beam Blank Modeling Features of 2D Beam Blank Uncoupled ThermoUncoupled Thermo--Mechanical ModelMechanical Model
Complex geometries produce additional difficulty in numerical modeling.
Austenite and delta-ferrite viscoplastic constitutive laws integrated in UMAT - Material Nonlinearity.
Temperature dependant material properties for 0.07 %C steel grade – Nonlinear Material Properties.
DFLUX subroutine imposing heat flux profile for good contact.Softened mechanical contact with friction coefficient 0.1-Boundary Nonlinearity.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 15
Realistic Temperature Dependant Material Properties
1000 1200 1400 16000.7
0.8
0.9
1
1.1
1.2
1.3
1.4x 10
6
Temperature [C]
Ent
halpy
[J/k
g]
Hf
1000 1200 1400 160030
32
34
36
38
40
Temperature [C]
Con
duct
ivity
[W
/mK
]
259.3 W/mK in Liquid
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 16Temperature (oC)
Ela
stic
Mo
du
lus
(GP
a)
0 200 400 600 800 1000 1200 1400 16000
20
40
60
80
100
120
140
160
180
200
1000 1100 1200 1300 1400 1500 16001.2
1.4
1.6
1.8
2
2.2
2.4x 10
-5
Temperature [C]
Coe
ffic
ient
of
The
rmal
Exp
ansi
on [
1/K
]
Imposed heat flux profile for good Imposed heat flux profile for good contactcontact
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 17
Steel Phase FractionsSteel Phase Fractions
Steel Grade: 0.07 %CTsol = 1471.9 C Tinit = 1523.7 C
Tliq = 1518.7 C T10%delta = 1409.2 C
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 18
Mechanical Contact Mechanical Contact
Based on “slave” (shell)
and “master” (mold) surfaces
Friction modeled with small
Softened Contact used due
to “soft” slave (shell) surface
frictμ
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 19
Schematics of Beam Blank Casting Schematics of Beam Blank Casting and the and the ““snakesnake”” FE Domain FE Domain
Uncoupled 2D Generalized Plane Strain Thermo-Mechanical Model Casting Speed 0.889 m/minWorking Mold Length 660.4 mm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 20
Shell Temperature Contour at Mold Shell Temperature Contour at Mold ExitExit
(play movie here)(play movie here)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 21
Shell Thickness Evolution HistoryShell Thickness Evolution History
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 22
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
Time Bellow Meniscus [Sec]
She
ll Thi
ckne
ss [m
m]
Point C
Point BMid Flange Point
Point D
Shell Stress Contours at Mold ExitShell Stress Contours at Mold Exit
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 23
Shell Shrinkage at Mold ExitShell Shrinkage at Mold Exit
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 24
No Mold Contact-Free Shell
With Mold Contact With Mold Contact with Negative Taper at Shoulder
Ideal Shrinkage (Taper) ProfilesIdeal Shrinkage (Taper) ProfilesNo Mold Contact CaseNo Mold Contact Case--Free ShellFree Shell
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 25
Ideal Shrinkage (Taper) ProfilesIdeal Shrinkage (Taper) ProfilesMold Contact CaseMold Contact Case
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 26
Ideal Shrinkage (Taper) ProfilesIdeal Shrinkage (Taper) ProfilesMold Contact Case with Negative Taper at Shoulder ImposedMold Contact Case with Negative Taper at Shoulder Imposed
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 27
Hot Tearing Failure Predicted by Inelastic Hot Tearing Failure Predicted by Inelastic Strain Results Strain Results
Hot tearing takes place in the mushy zone between 90% and 99% solid. [Thomas, Won, Li, 2000-2004].
Dendrite fingers are thick preventing surrounding liquid to feed into interdendriticspaces formed by thermal shrinkage of solid.
Damage strain can be calculated from inelastic strain difference for 90% and 99% solid and compared to empirical critical value to predict onset of hot tearing.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 28
Beam Blank Simulation ConclusionsBeam Blank Simulation Conclusionsthermo-mechanical model can evaluate temperature, stress, strain and deformation of a continuous casting beam blank with complex geometry.Point B (on the shoulder) has the thinnest shell, so is probably most prone to break-outs.Hoop stress results show expected compression on the surface and tension close to the solidifying frontDeformation (Shrinkage) results can be used to predict ideal mold taperAt the flange area, a large interfacial gap is forming which must be compensated by adequate taper. The inelastic strain in the mushy zone, can be extracted from these results and used with the proper fracture criteria to predict hot-tear cracks.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 29
ThermoThermo--Mechanical Model of Thin Slab CastingMechanical Model of Thin Slab Casting
Thermo-mechanical models of thin slab casting are very rare. The main additional modeling complication comes from the modeling transient geometry of the funnel shape
Only a proper 3D model can reveal the state of axial (casting direction) stresses responsible for internal transverse cracks in solid.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 30
3D Thin Slab Casting Modeling Details3D Thin Slab Casting Modeling DetailsUncoupled approach using the flux data compiled from the plant measurements.Mesh refinement study conducted to find the proper mesh to capture solidification phenomena in 3D fixed mesh (430,000 dofs).All time dependant properties are calculated with respect to local material point time
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 31
0.3 0.60. 0.9 1.2
Distance Bellow Meniscus [m]
Geometry and 3D FE modelGeometry and 3D FE model
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 32
Casting Speed 3.6m/min Strand Thickness 90mmWorking Mold Length 1100mm Funnel Depth Meniscus 40mmTaper 0%/m Funnel Depth Mold Exit 6mm
Deformation ResultsDeformation Results(play 2 movies here)(play 2 movies here)
Initial (black: at meniscus) and final (light green: at mold exit) shell shape 3-D view from bottom of mold
Central gap formation with temperature contour at14.5 sec., 3D side view on longitudinal central section
Detail corner bottom shell surface distortion with temperature contour imposed at 12 sec. bellow meniscus
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 33
Center Plane Solid Shell and Gap EvolutionCenter Plane Solid Shell and Gap Evolution
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 34
Temperature Contour and Temperature Contour and wfwf bottom edge distributions bottom edge distributions
when Bottom Plane at 5 and 19 sec. bellow meniscuswhen Bottom Plane at 5 and 19 sec. bellow meniscusMost of shell cooling uniformly except corner
Negligible heat conduction in casting direction.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 35
Transverse Stress Contours and Transverse Stress Contours and wfwf bottom edge bottom edge distributions when bottom plane is at 5,12, and 15.8 sec.distributions when bottom plane is at 5,12, and 15.8 sec.
2 Stress Reversals in funnel area (surf. tension/subsurf. compression) at 5 and 13-16s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 36
Axial Stress Contours and Axial Stress Contours and wfwf bottom edge distributions bottom edge distributions when bottom plane is at 5,12, and 15.8 sec.when bottom plane is at 5,12, and 15.8 sec.
Similar to Transverse Stress Situation, 2 Stress Reversals in Funnel at 5 and 13-16 s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 37
Stress Histories for Bottom Edge Stress Histories for Bottom Edge wfwf PointsPoints
center wf 0.31 m from center 0.58 m from center
2 4 6 8 10 12 14 16 18 20-10
-8
-6
-4
-2
0
2
4
6
8
10
Time Bellow Meniscus for Bottom Surface [Sec.]
Str
ess
es
for
Ce
nte
r S
urf
ace
Fu
nn
el P
oin
t [M
pa
]
Transverse Stress (S11)Axial Stress (S33)
2 4 6 8 10 12 14 16 18 20-8
-6
-4
-2
0
2
4
6
Time Bellow Meniscus for Bottom Surface [Sec.]
Str
ess
es
for
Fu
nn
el P
oin
t 0.3
1m
. fro
m C
en
ter
[Mp
a]
Transverse Stress (S11)Axial Stress (S33)
0 5 10 15 20-12
-10
-8
-6
-4
-2
0
2
Time Bellow Meniscus for Bottom Surface [Sec.]
Str
esse
s fo
r a
poin
t on
str
aigh
t pa
rt o
f w
f 0.
58m
fro
m C
ente
r [M
pa]
Transverse Stress (S11)Axial Stress (S33)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 38
Thin Slab Simulation ConclusionsThin Slab Simulation ConclusionsA significant interfacial gap at and near the corner, on the narrow face, owing to the lack of mold taper.Another smaller gap was recorded at the center of wf. Large gradients of temperature between the corner tip and wider corner area causing uneven shell developmentNegligible temperature gradients in the casting directionjustifying the 2D assumption of negligible heat conduction in axial (casting) directionBesides usual thermo-visco-plastic stresses coming from solidification due to the uneven cooling through shell thickness, there is a strong pure mechanical component coming from the funnel geometry pushing and bending solidified shell. Two periods of stress reversals, characterized by the surface tension and the subsurface compression, are revealed for both transverse and axial shell stresses in the funnel area. The transverse stress reversals in funnel mold are mostly consistentwith the findings of Park 2002. The axial stress results are novel !
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 39
Future Work Recommendations Future Work Recommendations Apply the more realistic heat flux profile along with the measured plant taper data to model the realistic plant conditions, and compare with available real-world beam-blank shell failures.Apply increment-wise 2D coupled thermo-mechanical model, which have been already developed and tested, that would enable even more accurate modeling, especially for the gap formations.Apply the models from this work to solve variety of practical continuous casting problems and improve the process efficiency and quality of the products:
-taper optimization-prediction of breakouts due to shell thinning in hot spots-understanding the causes of surface depressions and longitudinal cracks-development of transvrs. cracks due to withdrawal forces overcoming friction-hot tearing crack prediction in mushy/liquid zone -thermo-mechanical behavior of solidifying shell bellow mold and more…
Abaqus Inc. is providing fluid-solid interface (FSI) capabilities. This would enable a fully coupled fluid-thermal-mechanical analysis with Fluent and Abaqus using this model.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 40
Practical Application Example Using Similar Numerical Practical Application Example Using Similar Numerical 2D Models: 2D Models: Critical Billet Casting Speed to Avoid Longitudinal Critical Billet Casting Speed to Avoid Longitudinal
CracksCracks [Park, Thomas, C. Li, [Park, Thomas, C. Li, SamarasekeraSamarasekera, 2002], 2002]
Longitudinal corner crack
(forms in mold, large corner radius)
Off-corner internal crack
(forms bellow mold, small corner radius)
Based on hot tearing criterion
Based on 1mm maximum center bulging
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 41
Acknowledgments:Acknowledgments:
Prof. Brian G. Thomas
Chungsheng Li, Hong Zhu, and Kun Xuformer (and current) UIUC students
National Center for Supercomputing Applications
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seid Koric 42