ANNUAL REPORT 2010ANNUAL REPORT 2010ccc.illinois.edu/s/2010_Presentations/14...University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • BG Thomas 19 r Container

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


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


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



Tensile StrainStrain

Tensile strains develop perpendicular to dendrite

growth directiong





Pierer R., Michelic S., Bernhard C. A Hot Tearing Criterion for the Continuous Casting Process, Private Communication.



Bernhard C.:Anforderungen an prozessorientierte Heißrissbildungsmodelle BHM, Vol. 149 (2004), 90-95


SSCC Test

Final Shell ShapeFinal Shell Shape


Removed Solidified Shell

Half 1 Half 2Half 1 Half 2


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


, , , , ,

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


* 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


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)


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


Met. Trans. A, Vol. 23A, 1992, pp. 903-918.

Model Validation


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


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


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.


r

Temperature History – PP05

z

r

Note short delay

in Tincrease (immersion).

TC TM

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • BG Thomas 21r

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


r

Stress Perpendicular to Shell Growth Direction, 25 sec,

z

Stress is location

and time dependant.


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


UP 1 Temperature, UP 1

-41300


6

1500

1550

C

L+δ+γL+δL

-21300


UP 1UP 1 Temperature, UP 1

-41300


6

1500

1550

C

L+δ+γL+δL

-21300


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


Z,Z

25 secStress, UP 2

Stress, LP 1

Stress, LP 2

-2

0

1300

1350

0 2 4 6 8 10

Tem


Z,Z

25 sec

z


rr

Spatial and temporal variant temperature and stress profile.

Solidification Force

( )# nodes

Sol Force Reaction Force ( )i=1

Sol. Force= Reaction Forcei


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 !


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.


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


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


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


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


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!!!!


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.


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


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


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


Lance Hibbeler, Seid Koric

Documents

ANNUAL REPORT 2010ANNUAL REPORT 2010ccc.illinois.edu/s/2010_Presentations/14...University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • BG Thomas 19 r Container