uiuc, august 12, 2010 review of longitudinal facial...

ANNUAL REPORT 2010ANNUAL REPORT 2010UIUC, August 12, 2010

Review ofLongitudinal Facial CrackingLongitudinal Facial Cracking

and

Lance C. Hibbeler and Hemanth Jasti

Preliminary Crack SimulationsLance C. Hibbeler and Hemanth Jasti(Ph.D. Student) (MSME Student)

Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaign

Objectives

• Review mechanisms for longitudinal cracks in continuously cast steel

• Simulate crack formation using thermo-Simulate crack formation using thermomechanical FE model

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

Cracks in Continuously Cast Steel

Cracks form by combination of 1) tensile stress and

2) metallurgical embrittlement2) metallurgical embrittlementSurface Cracks (initiated in the mold)

Transverse cornerTransverse surfaceLongitudinal midfaceLongitudinal off cornerStar

Internal cracks (initiated at solidification front)

Off corner (subsurface)

Midway StraighteningPinch roll

BG Thomas

Radial streaks

Centerline Triple point Diagonal

Longitudinal Facial Cracks (LFCs) g ( )

Front

100 mm

Top

Some LFCs have depressions Some don’t


Brimacombe & Sorimachi, Met Trans B, 8B, 1977, pp 489-505

Longitudinal Facial Cracks in Continuous CastingContinuous Casting

Front Top

100 mm

OuterFlat

InnerCurve

OuterCurve

InnerFlat

InnerCurve

OuterCurve

OuterFlat

◊○□

∆ ∆□

⌂ ⌂ ⌂⌂ ⌂⌂ ⌂○ ○◊ ◊

Mode Symbol Location Notes

⌂∆ ∆□ □ □⌂ ⌂ ⌂ ⌂ ⌂ ⌂○ ○ ○ ○○◊ ◊ ◊ ◊

Mode Symbol Location Notes

I ◊ Inside Curve Funnel only; depression-type; excessive bending

II ○ Outside Curve Funnel only; depression-type; excessive NF taper

III ⌂ No Preference Jagged, short cracks; heat transfer related


IV □ Near SEN Fluid-flow related

V ∆ Off-Corner WF Inadequate NF taper

Corus IJmuiden Plant ExperienceLFC Breakout Locations

22Inner Flat Inner Curve Outer Curve Outer Flat

Data provided by A. Kamperman of Corus

LFC Breakout Locations

16

18

20

ak

ou

ts (

%) Inner Flat Inner Curve Outer Curve Outer Flat

Mode I

10

12

14

tal L

FC

Bre

a

January 2005 - August 2007

4

6

8

nta

ge

of

To

t

Mode IV

Mode V

0

2

4

0 100 200 300 400 500 600 700

Pe

rce

n

Mode II


Distance from Center (mm)

Each interval is 10 mm. Shows the locations of depression-type LFC’s that caused breakouts

Longitudinal Facial CrackingDepression Mechanism (Type I II)Depression Mechanism (Type I, II)

• Root cause is non-uniform heat transfer• Initiate nonuniformity (shell depression)Initiate nonuniformity (shell depression)

– Variations in slag rim thickness at meniscus– Gap from necking (mold friction issues)

G f b kli ( i NF t )– Gap from buckling (excessive NF taper)

• Depression causes:– Lower heat flux

Mo

ld W

Mo

ld W

– Higher shell temperature– Thinner shell– Grain growth (larger grains)

Amplifies if the shell buckles

Wall

Wall

Grain growth (larger grains)– More brittle behavior– Stress and strain concentrations

• Tensile inelastic strain exceeds critical

Combination causes cracks


• Tensile inelastic strain exceeds critical value cracks form

Longitudinal Facial Cracks

• Mechanism:High tensile strains & stresses in the solidifying shell– High tensile strains & stresses in the solidifying shell at the meniscus, due to high heat transfer and/or non-uniform shell growth. Mainly thermal in origin

• Influencing factors (worse with):– peritectic steels (0.08-0.15%C)

high S level or low Mn/S ratio < 25– high S level or low Mn/S ratio < 25– high or variable casting speed– Metal level fluctuations– Mold powder, taper, oscillation problems– Overcooling in sprays– Insufficient submold support BG Thomas


Insufficient submold support– Poor alignment (especially between mold & submold)

BG Thomas

Causes ofNonuniform Mold Heat TransferNonuniform Mold Heat Transfer

• Level fluctuations (fluid flow problems, too-shallow submergence depth etc )submergence depth, etc.)

• Mold hotface variations around perimeter at meniscus– Mold water slots (slot variations, cold mold water)

M ld t lit (l l l l i h l t l l– Mold water quality (local scale plugging a channel, etc. cause local variations

• Superheat variations• Abrupt speed changes• Excessive heat removal (makes variations more likely)• Insufficient heat SEN preheat causing meniscus bridgingInsufficient heat SEN preheat causing meniscus bridging

(Robinson 1994)

BG Thomas


BG Thomas

High Temperature Embrittlement


BG Thomas

Mechanism of Longitudinal CrackingLongitudinal Cracking

Metal level

Casting direction Sideview

(mainly Mode III)

Mold wallTopview

(mainly Mode III)

shell

BG Thomas

view


BG Thomas

Location of Crack Formation

Liquidus

Solidus

Liquidus

x1start

Strand surface

x2x1

1

Internal

x2

Internal crack

end

High TemperatureC

BG Thomas


High Temperature Zone of Low Ductility

Casting Direction

Longitudinal Corner Cracks(Type V)( ype )


Brimacombe & Sorimachi, Met Trans B, 8B, 1977, pp 489-505

Longitudinal Corner Cracks(Type V)

• Mechanism: Hoop stresses around large corner gap due to locally thin, embrittled shell at corner allow

( ype )

gap due to locally thin, embrittled shell at corner allow internal cracks to propagate through

• Influencing factors (worse with):– Large corner radius– Insufficient taper (generates corner gap in upper

mold which reduces heat transfer there))– Steel with 0.17-0.25%C, S>0.035%; P>0.035%

• Solution: Decrease corner radius to 3 4 mm– Decrease corner radius to 3-4 mm

– Optimize taper (use double or parabolic design)

BG Thomas


BG Thomas

Depression Mechanisms• Inside curve:

– Friction + bending pins the shell at the transition pointsM ld i d b kli if l l h ll h i k i t h t t h th– Mold may induce buckling if local shell shrinkage is not enough to match the mold perimeter length change

• Outside Curve 1

2

3

• Outside Curve– Friction + bending pins the shell at the inside/outside curve transition point– Excessive NF taper causes the shell to lift off the mold surface, reducing

heat transfer

1

– Bending (funnel and ferrostatic pressure) causes tensile stress on surface, leads to necking


Excessive Narrow Face Taper

• Shell under compression once the narrow face comes into good contact with the shell– Occurs earlier with deeper crowns

– Tends to cause buckling, leads to other problems 0.5

Excessive

-10

-0.5

0.0

tres

s (M

Pa)

30 mm

20 mm

Mold

Shell

Excessive NF Taper

-2.0

-1.5

1.0

Ave

rage

St

20 mm Crown

30 mm Crown

40 mm Crown

40 mm


-2.5

0 1 2 3 4 5 6 7 8 9 10 11

Time (s)Gap

Stress Profiles and HistoriesThrough Thickness in Flat RegionsThrough Thickness in Flat Regions

2

4

62 s

4 s 6 s 8 s 10 s

Tensile Stress

• After initial tensile load, surface stays in compression

-4

-2

0

2

tre

ss

(M

Pa

)

Compressive Stress

Tensile Stress stays in compression

• Solidification front is always under tensile loading

N t t th h thi k i

6

12

-10

-8

-6

St • Net stress through-thickness is

always zero

• Soft delta-ferrite unable to carry a -2

0

2

4

(MP

a)

-12

0 2 4 6 8 10 12 14 16

Distance Beneath Shell Surface (mm)

substantial load

• Stress peaks after transition to the austenite phase

-10

-8

-6

-4

Str

es

s 0.0mm 1.5mm 3.0mm 4.5mm 6.0mm 7.5mm


• By mold exit, only the first 2 mm of the shell are in compression

-12

0 1 2 3 4 5 6 7 8 9 10 11Time (s)

Surface Stress Around Perimeter:Effect of Funnel Width

8.0750 mm Outer Funnel Width950 O t F l Width

Effect of Funnel Width

4.0

MP

a)

950 mm Outer Funnel Width

2 s

-4.0

0.0

ce S

tres

s (M

-8.0

Sh

ell

Su

rfac

4 s

6 s

8 s

-16.0

-12.0

S

10 s


0 50 100 150 200 250 300 350 400 450 500 550 600 650

Distance from Mold Centerline (mm)Stress component perpendicular to temperature gradient (tangent to mold surface)

Stress Near Solidification Front:Effect of Funnel Width

8.0750 mm Outer Funnel Width

Effect of Funnel WidthPeak stress (in γ phase)

6.0

7.0(M

Pa)

950 mm Outer Funnel Width

4.0

5.0

hel

l S

tres

s (

4 s

6 s

2.0

3.0

axim

um

Sh

8 s

0.0

1.0

Ma

2 s

10 s


0 50 100 150 200 250 300 350 400 450 500 550 600 650

Distance from Mold Centerline (mm)Stress component perpendicular to temperature gradient (tangent to mold surface)

Funnel Bending Effect

• A unique attribute of funnel molds is that the steel h ll i i ifi tl b t it lid d thshell is significantly bent as it slides down the

mold

Tension

Compression

Compression

TensionCompression

• Beam theory from solid mechanics can elucidate the important parameters in the phenomenon

y

x2·h

This end pinned, u = 0M

εmax, compressive

εmax, tensile

x

y

Rε = −


w

εmax, compressive R

[R.C. Hibbeler, Mechanics of Materials, 5e, 2003]

Strain Decomposition:Identify Bending EffectIdentify Bending Effect

Centerline Inside Curve


total thermal mechanical thermal elastic inelastic= + = + +ε ε ε ε ε ε

Analytical Bending Model:Comparison with Numerical ModelComparison with Numerical Model

• Take the difference between bending a beam 0 70

0.0 2.2 4.4 6.6 8.8 11.0Time Below Meniscus (s)

between bending a beam to the funnel radius at the meniscus and the funnel radius at some other depth: 0.50

0.60

0.70

Str

ain

(%

)

Analytical ModelNumerical Model

radius at some other depth:

( ) ( )( )

( )( ) ( ) ( ) ( )

( ) ( )meniscus

bendingmeniscus meniscus

z z r z r zz z

r z r z r z r z

δ δε δ

−= − =

0.30

0.40

al B

en

din

g

h

750 mm OuterFunnel Width

δ = distance from neutral axis ≈ shell thickness 0.00

0.10

0.20

Me

ch

an

ic

En

d o

f fu

nn

el l

en

gth


( )2( )

( )4 16 ( )

outer funnel width inner funnel widthcrown zr z

crown z

−= +

⋅

• Compare with results of 2D model with the thermal

Bending Strain on Solidification Front

0 200 400 600 800 1000

Distance Below Meniscus (mm)


model with the thermal effects subtracted

Analytical Parametric StudyLarger total funnel width = Larger radius = Lower bending strain and strain rate

Shallower funnel = Larger radius = Lower bending strain and strain rateLonger Funnel = Increases strain near bottom of funnel (larger radius for more time), but lowers strain rate

0 40

0.50

0.60

0.70

0.80750 mm Outer Funnel Width850 mm Outer Funnel Width950 mm Outer Funnel Width

nd

ing

Str

ain

(%

)

0 40

0.50

0.60

0.70

0.80260 mm Inner Funnel Width130 mm Inner Funnel Width0 mm Inner Funnel Width

nd

ing

Str

ain

(%

)

0 50

0.60

0.70

0.80

0.90

1.00

30 mm Crown at Top20 mm Crown at Top10 mm Crown at Top

nd

ing

Str

ain

(%

)

En

d o

ffu

nn

el l

en

gth

0 40

0.50

0.60

0.70

0.80

nd

ing

Str

ain

(%

)

130 mm InnerFunnel Width


8 mm Crownat Bottom

0 00

0.10

0.20

0.30

0.40E

nd

of

fun

ne

l le

ng

th

Me

ch

an

ica

l B

en

0.00

0.10

0.20

0.30

0.40

En

d o

ffu

nn

el l

en

gth

Me

ch

an

ica

l B

en

0.00

0.10

0.20

0.30

0.40

0.50

Me

ch

an

ica

l B

en

0.00

0.10

0.20

0.30

0.40

850 mm Funnel Length



Me

ch

an

ica

l B

en

0.00

0 200 400 600 800 1000Distance Below Meniscus (mm)

0 10

0.12

0.14

750 mm Outer Funnel Width850 mm Outer Funnel Width950 mm Outer Funnel Width

hn R

ate

(%

/s)

0.00


0 10

0.12

0.14260 mm Inner Funnel Width130 mm Inner Funnel Width0 mm Inner Funnel Width

h Ra

te (

%/s

)

0.00


0.12

0.15

n R

ate

(%

/s)

En

d o

fn

ne

l le

ng

th

0 10

0.12

0.14

850 mm Funnel Length950 mm Funnel Length1050 mm Funnel Length

Ra

te (

%/s

)

0.00


0.04

0.06

0.08

0.10

En

d o

ffu

nn

el l

en

gt

an

ica

l B

en

din

g S

tra

in

0.04

0.06

0.08

0.10

En

d o

ffu

nn

el l

en

gth

nic

al

Be

nd

ing

Str

ain

0.03

0.06

0.09

30 mm Crown at Top20 mm Crown at Topa

nic

al

Be

nd

ing

Str

ain fun

0.04

0.06

0.08

0.10

nic

al

Be

nd

ing

Str

ain


0.00

0.02


Me

ch

a

0.00

0.02


Me

ch

a

0.00

0.03

0 200 400 600 800 1000

p10 mm Crown at Top

Distance Below Meniscus (mm)

Me

ch

a

0.00

0.02


Me

ch

a

Subsurface Hot Tears

• Typical solidification stresses put tension on the lidifi ti f tsolidification front

– Tension increased by bending effect in inner curve region thus higher risk of hot tearingregion, thus higher risk of hot tearing

• Critical hot tearing strain quantified by Won:0.02821=ε Won et al., Metall. Mat. Trans., 31B:4 (2000), pg. 779

• Brittle temperature zone (BTZ):

0.3131 0.8638=

⋅ΔcBT

εε

Brittle temperature zone (BTZ):

• Average inelastic strain rate in BTZ:

( 99%) ( 90%)B s sT T f T fΔ = = − =


g( 99%) ( 90%)

( 99%) ( 90%)s s

s s

f f

t f t f

ε εε = − === − =


• Extremely fine mesh required to apply Won model (0.06 mm element size is insufficient)– Use 1D numerical model to calculate temperatures and

inelastic strain profile history in flat regions of moldinelastic strain profile history in flat regions of mold

– Add bending effect with analytical model

• Low-carbon steels exhibit strong numerical noiseLow carbon steels exhibit strong numerical noise– Use a higher carbon grade (0.07%C) to reduce effect

– High-carbon grades are also more crack-sensitiveg g

• Define “damage index” as ratio of actual damage strain to critical damage strain (crack forms at


unity)dmg cD ε ε=( 99%) ( 90%)dmg s sf fε ε ε= = − =


• No hot tears will form under normal operation 0.20

0.25

(%/s

)

Parallel MoldNominal Funnel Mold200 mm Wider Funnel100 mm Longer Funnel

0.10

0.12

under normal operation– Bending effect increases

likelihood of cracks

• Most likely place is just0.10

0.15

nel

asti

c S

trai

n R

ate

( 100 mm Longer Funnel

0.04

0.06

0.08

Dam

age

Str

ain

(%

)

Parallel MoldNominal Funnel Mold• Most likely place is just

a few mm subsurface• Funnels more

tibl t h t t

0.00

0.05

0 1 2 3 4 5 6 7

Distance From Shell Surface (mm)

Avg

. In

0.00

0.02

0 1 2 3 4 5 6 7


Nominal Funnel Mold200 mm Wider Funnel100 mm Longer Funnel

susceptible to hot tears:– Narrower funnel width

(higher bending strain)D (hi h

2.00

2.50

3.00

rain

(%

)


0.06

0.08

0.10

x (-

-)

– Deeper crowns (higher bending strain)

– Longer (higher strain rate when mushy zone is

0.50

1.00

1.50

Wo

n C

riti

cal S

tr

0.02

0.04

Dam

ag

e In

dex



when mushy zone is large)

0.00

0 1 2 3 4 5 6 7


0.00

0 1 2 3 4 5 6 7


Implications on Funnel Design

• This effect is proportional to the funnel radius– Larger radius = lower cracking tendency

• Also affected by funnel shape in casting direction– Want more change in shape close to the meniscus when

the mushy zone is still small

– “Radiused” style better than “linear”Radiused style better than linear

• These subsurface cracks propagating through the shell are the likely mechanism behind a depressionshell are the likely mechanism behind a depression evolving into a breakout


Implications on Funnel Design• A larger funnel radius provides:

– More uniform heat transfer– Smaller bending effect in the transition region– Lower tendency to form subsurface hot tears

• A “better” funnel (with respect to depression type• A better funnel (with respect to depression-type LFCs) has a wide funnel and small crown

D

Increase outer funnel widthDecrease crown funnel width

( )2( )

( )outer funnel width inner funnel widthcrown z −

• Depression-related LFCs are also affected by f i ti d f t

Decrease inner funnel width

( )( )( )

4 16 ( )

f fcrown zr z

crown z= +

⋅

friction, and narrow-face taper• Many other phenomena can cause LFCs

Crack Simulation Domain

Moving displacement with straight line enforced

Insulatedq=0

Stress free

Solidification

Solidification CrackFixed qmold

CrackInsulatedq=0

Displacement


q=0

H Jasti

Initiate a Depression with Nonuniform Heat TransferNonuniform Heat Transfer

• Varies with distance • Varies with time inVaries with distance away from the crack

Varies with time in mold

1

1.2

ld

Fraction of qmold applied

1

1.2

d

Fraction of qmold at crack edge over time

0.4

0.6

0.8

acti

on

of

qm

ol

0.4

0.6

0.8

1

ctio

n o

f q

mo

ld

0

0.2

0 10 20 30

Fra

Di t f C k ( )

0

0.2

0.4

0 2 4 6 8 10

Fra

c

Ti ( d )


Distance from Crack (mm) Time (seconds)

H Jasti

Depression SimulationsVertical direction inelastic strain, 0.75 mm tensile displacement superimposed on solidification shrinkage

Heat flux locally decreased BY 50% Heat flux locally decreased BY 80%


H Jasti

y Heat flux locally decreased BY 80%

Greater decreases in heat flux lead to deeper depressions

Depression Simulation

• Case with 80%Case with 80% reduction in heat flux produces reasonable depression shapedepression shape– However, comparison is

with a cold sample

Brimacombe et al., MMTB 1979


H Jasti

Study of Depression Behavior

• Greater decreases in heat flux lead to deeper depressions– Differences not significant until mold exit


H Jasti


• Increasing superimposed tensiledisplacement makes depressions deeper– Necking phenomenon

Effect of Applied Tension Strain on Depression

0 2

0.30

0.35

0.40

0.45

Mol

d Fa

ce (m

m)

Effect of Applied Tension Strain on Depression

0.05

0.10

0.15

0.20

0.25

Dis

plac

emen

t fro

m M 0.75mm displacement

0.25mm

0.50mm

1.0mm


0.00

0 5 10 15 20 25 30 35

Distance from Crack Edge (mm)H Jasti


• Decreasing applied heat flux under superimposed compressive displacement causes deep depressions via buckling

Effect of Heat flux Uniformity on Depression Creation with Compressive Strain

1 5

2

2.5

3

3.5

old

Face

(mm

)

Creation with Compressive Strain

20% of Average Heat Flux at Crack50%

-1

-0.5

0

0.5

1

1.5

spla

cem

ent f

rom

M

50%

80%

100%


H Jasti

-1.5

1

0 5 10 15 20 25 30 35

Dis

Distance from Crack Edge (mm)

Cracking Potential

• Damage index increases with increasing i d t il di l t dsuperimposed tensile displacement and

increasing drop in heat fluxC ki i i i t d t i• Cracking is imminent under certain conditions (strong imposed tension)

0 20

0.25

0.30

0.35

nd

ex

Ideal Casting

0 75 Di d1

1.2

1.4

1.6

Ind

ex

0.75mm Dis with HF drop to 20% at crack

0 00

0.05

0.10

0.15

0.20

Dam

age

I 0.75mm Dis and 50% HF drop at crack

0.75mm displacement

0% HF d 0

0.2

0.4

0.6

0.8

Dam

age

I

0.75mm Dis over 4 secs and HF drop to 50% at crack during same 4 secs


0.00

0 1 2 3 4 5 6 7 8 9 101112131415

Distance from Shell Surface (mm)

50% HF drop at crack

0

0 1 2 3 4 5 6 7 8 9 10Distance from Shell Surface (mm)

H Jasti

Conclusions - 1

• Five families of LFCs have been observed– I. Funnel molds: inner curve depressions

• Lessen with larger horizontal funnel radius

– II. Funnel molds: outer curve depressions• Lessen by optimizing taper

– III. Heat transfer related

– IV. Fluid flow related near SEN

– V. Taper related near NF


Conclusions - 2

• Depressions can be formed from severe local drops in heat flux– Superimposed tension (insufficient taper) leads

to slightly deeper depressions

– Superimposed compression (excessive taper) leads to much deeper depressions

• However, cracks require tension to form, so either subsurface cracks propagate through the shell or something is very wrong at the


shell surface

Acknowledgements

• Continuous Casting Consortium Members (ABB Arcelor Mittal Baosteel Corus LWB(ABB, Arcelor-Mittal, Baosteel, Corus, LWB Refractories, Nucor Steel, Nippon Steel, Postech Posco ANSYS-Fluent)Postech, Posco, ANSYS-Fluent)

National Center for Supercomputing• National Center for Supercomputing Applications (NCSA) at UIUC – “Abe” cluster

• Dassault Simulia, Inc. (ABAQUS parent company)


company)

uiuc, august 12, 2010 review of longitudinal facial...

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