CCC Annual ReportUIUC, August 14, 2013

Lance C. HibbelerPh.D. Student and Lecturer

Department of Mechanical Science & Engineering

University of Illinois at Urbana-Champaign

Mechanical Behavior of the Mushy

Zone of Solidifying Steel

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 2

Introduction

• Hot tearing is a solidification defect that leads to

poor product quality at best and a breakout at worst

• The averaging in traditional macro-scale models –

mushy zones – prevents study of the details of hot

tear formation and propagation

• This work explores hot tears with a micro-scale

model – of the dendrites themselves – by

combining macro-scale information with a detailed

model of the morphology of the solidification front

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 3

Modeling Approach

Casting

conditions

CON1DSolidification with mushy zone

and ideal taper

• 1D FDM energy equation

MICRESSSolute diffusion, solidification

with dendrite morphology

• 2D FVM phase field

• 1D FVM energy equation

Slab surface

temperature

macromicro

ABAQUSSolidification with mushy zone,

thermo-mechanical slice model

• 2D FEM energy & momentum

macro

ABAQUSDetailed mechanical behavior of

liquid, solid, and dendrites

• 2D FEM energy & momentum

micro

Dendrite morphology,

mush temperatures

Bulk shrinkage

Eulerian

Lagrangian

Lagrangian

Lagrangian

HibbelerHeat conduction outside

of MICRESS window

Slab surface heat flux

Temperature

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 4

Microscale Domain and BC

x

y Fixed edge, uy = 0, σxy = 0

Generalized plane strain edge, uy = uniform, σxy = 0

Solid

LiquidFix

ed e

dge,

ux

= 0

, σ

xy

= 0

Fre

e e

dge,

σxx

= 0

, σxy

= 0

66 µ

m

333 µm

Phase field calculated with MICRESS by B. Boettger

Out-of-plane assumption: generalized plane strain uz = uniform

200,000 4-node elements, 0.3-µm square

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 5

Explicit Finite Element Method

Get accelerations

from force balance

Integrate to get

half-step velocity

Integrate at half-step

to get displacement

Efficiencies from:

• No Newton iterations (no matrix solve)

• Lumped mass matrix (no matrix solve)

• Mass scaling – make density large to increase critical step size

Critical time step

Dilational wave speed

(approx. 1000 m/s)

Koric, Hibbeler, Thomas

IJNME 2009

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 6

Modeling Issues

• ABAQUS/Explicit has trouble with the formation of

the first solid material, but the explanation is more

evident than with ABAQUS/Standard:

– The large step-change in stiffness causes the critical time

step to be violated

• The mass scaling must be readjusted, frequently, to

account for the change in stiffness as temperature and

phase evolve

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 7

Modeling Issues

• Imposing the generalized plane strain constraint

prevents parallelization (in ABAQUS/Explicit)

• Efficient solution to this problem is to calculate the

shrinkage in a macroscale model (with mush) and

impose time-dependent boundary conditions

200,000 8-node elements, 0.3-µm cube

x

y zTop face fixed in z

Other BCs mimic 2D case

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 8

Material Models

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7 8 9 10

Strain (%)

Str

es

s (

MP

a)

Austenite

δ-Ferrite

Strain Rate = 10-4

s-1

Temperature = 1400 °C

Composition = 0.045 %wt C

• Liquid:

– Nearly-incompressible Newtonian fluid

• Solid– Zhu (ferrite) or Kozlowski III (austenite)

( ) ( ) ( )( )

( ) ( )

( )

( )

( )

32

411

1

3

1

3

2

3

3

4 4 5 2

4.465 10s exp

130.5 5.128 10

0.6289 1.114 10

8.132 1.54 10

( ) 4.655 10 7.14 10 1.2 10

f Tf T K

f C f TT

f T T

f T T

f T T

f C C C

ε σ ε ε−−

−

−

−

× = − −

= − ×

= − + ×

= − ×

= × + × + ×

&

( ) ( )

( ) ( )2

5.521

5.56 104

5

4

0.1 ( ) 300 (1 1000 )

1.3678 10

9.4156 10 0.3495

1 1.617 10 0.06166

nms f C T

f C C

m T

n T

ε σ ε

−

−−

− ×

−

−

= +

= ×

= − × +

= × −

&

Zhu

Kozlowski

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 9

Macroscale Slice Model

Prescribed heat flux

Insulated

Insulated Insula

ted

Thermal Boundary Conditions

Str

ess-F

ree

Equal perpendicular displacement

Zero perpendicular displacement

Zero perpendicular displacement

Mechanical Boundary Conditions

• Material properties from CON1D

• Mushy zone solidification

Domain

Liquid material

Solid material

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 10

Macroscale Model Results

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 11

Macroscale Total Strain

• Extract the total strain and its rate from the macroscale model

• Use piecewise approximation to eliminate noise from solidifying nodes

�� � �0.1135� � 0.0035

�� � �0.0076� � 0.0020

�� � �0.0030ln � � 0.0083

�� � 0 0s � � � 0.03s

0.03s � � � 0.05s

0.05s � � � 0.34s

0.34s � � � 10.0s

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 12

• MICRESS uses a moving Eulerian (spatial)

description, where the mesh follows the

solidification front of stationary material

• ABAQUS uses a Lagrangian (material) description,

where the mesh is fixed on the material

Descriptions of Motion

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 13

Eulerian—Lagrangian Conversion

• The “window” of data from MICRESS is patched into an ABAQUS domain according to how the Eulerian simulation has moved

Fraction Solid = 1 Fraction Solid = 0MICRESS Fraction Solid = f(x,y)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 14

Eulerian—Lagrangian Conversion

• Outside of the MICRESS window, the 1D heat conduction equation is solved with temperature and heat flux boundaries

• In the Python script that builds the ABAQUS file

• Temperature is continuous at boundaries of MICRESS window

MICRESS Temperature = f(x)

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��� ! � �"#$%!��� ! � �"#$%! �

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University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 15

Eulerian Dendrite Movement

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 16

Acknowledgments

• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, MagnesitaRefractories, Nippon Steel and Sumitomo Metal Corp., Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent)

• National Center for Supercomputing Applications (NCSA) at UIUC

• Dr. Bernd Boettger, ACCESS e.V.– See (Boettger, Apel, Santillana, and Eskin, MCWASP XIII) for more detail