modeling and simulation of microstructure evolution in solidifying …€¦ · stochastic modeling...

Modeling and Simulation of Microstructure

Evolution in Solidifying Alloys

Dr. Laurentiu Nastac

Concurrent Technologies CorporationPittsburgh, PA, USA

1020 atoms / mm3 of metal0.1 mm

Macro (1 mm-1m)

Micro (10-1000 mm)

Meso (0.1-10mm)

Length Scales

Summary of Predictive Capabilities

PREDICTION OF STRUCTURE

GRAIN AND

PARTICLE SIZE

INTERPHASE

SPACING

STRUCTURAL

TRANSITIONS

gray-to-white in cast iron

columnar-to-equiaxed

small grains-to- large grains

AMOUNT

OF PHASES

Coarsening Coalescence

Secondary Phases

carbides, eutectics,

porosities, etc.

Primary Phases

eutectics, etc.

Stochastic Modeling

Deterministic Approaches Probabilistic Approaches

Continuous Nucleation

Grain Growth and Orientation

interlamellar spacing in eutectics and eutectoids

dendritic arm spacing

Structure/Mechanical

Properties Database

Strength

Hardness

Fatigue

etc.

Empirical

Predicted and Experimental (DTA

Samples) SDAS for RS5 Alloys

m21 3 S St / 06

S 10x8.15μ

Secondary Dendrite Arm Spacing in VAR and

ESR Alloy 718 Ingots

VAR ESR

Prediction of PDAS and SDAS in VAR

Alloy 718 Ingots

μm μmPDAS SDAS

Prediction of Primary and Secondary

Dendrite Arm Spacings in Ti Ingots

1

10

100

1000

10000

1.E-05 1.E-04 1.E-03 1.E-02

V [m/s]

1 [m

m]

Ti-17

Ti-6-4

G=103 K/m

G=104 K/m

PAM Ingots

10

100

1000

1 10 100 1000 10000ts [s]

2 [m

m] Ti-6-4

Ti-17 PAM Ingots

Equiaxed dendrite

In Ti-17 ingots

Ti-17 =5 Al-2 Sn-2 Zr-4 Mo-4 Cr

Prediction of Primary and Secondary Arm

Spacings in Ti Ingots – Fe Effect

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

0 0.1 0.2 0.3 0.4Fe Content [wt.%]

PD

AS

Co

eff.

Ti-6-4

Ti-17

1.00E-05

3.00E-05

5.00E-05

7.00E-05

9.00E-05

0 0.1 0.2 0.3 0.4

Fe Content [wt.%]

SD

AS

Coef

f.

Ti-6-4

Ti-17

Prediction of PDAS and SDAS in PAM

Ti-17 Ingots

PDASSDAS

Microsegregation of Cr and Mo in Ti-17

Ingots – cooling Rate Effect

3.00

3.20

3.40

3.60

3.80

4.00

4.20

4.40

4.60

4.80

5.00

0 10 20 30 40 50 60 70 80 90 100

Data points or fS (vol. %)

Cr

(wt.

%)

Surface

Center Cra = 3.45-3.46%

3.50

3.70

3.90

4.10

4.30

4.50

4.70

4.90

5.10

5.30

5.50

0 10 20 30 40 50 60 70 80 90 100

Data points or fS (vol. %)M

o (

wt.

%)

Surface

CenterMoa = 4.18-4.34%

Solidification Map Development

Casting Conditions-superheat

-mold condition

-casting geometry

-withdrawal rate

-power input

Numerical Analysis / Experiments

Solidification StructureMacrostructure-grain size and direction

-grain morphology

Microstructure -spacing

-secondary phases

Solidification Conditions-liquid-solid (L/S) interface velocity

-temperature gradient at TL

-local cooling rate at TL

-bulk and surface nucleation

-fluid flow near the L/S interface

Mechanical

Properties

Predicted Solidification Maps

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

V [m/s]

G [

K/m

]

Fully

Equiaxed

Fully

Columnar Mixed

Solidification map for alloy Ti-6-4

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

V [m/s]

G [

K/m

]

Fully

Equiaxed

Fully

ColumnarMixed

Solidification map for alloy Ti-17

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

V [m/s]

G [

K/m

]

Fully

Equiaxed

Fully

Columnar

Mixed

Solidification map for alloy IN718

Why Use Stochastic Modeling?

Heterogeneous nucleation of grains

continuous

probabilistic nature

Crystallographic effects

growth anisotropy (grain selection/preferential growth)

probabilistic nature of grain extension

Nucleation and grain growth competition of various phases

(columnar/equiaxed/defects)

Glicksman’s Dendritic Growth

Experiments (Met Trans, 1988)

• Typical SCN dendrites (tree-like morphology)

Parallel to gravity

(symmetric dendrite)Different growth angle

(asymmetric dendrite) Magnification 13.5 times

Stochastic Mesoscale Modeling (Mod.

CA, Nastac, Acta Met, 1999)

Neighborhood Configurations

A-rhomboidal

B-square

C-hexagonal

Grain Patterns

A B

C

A B

C

Micro-model characterization:

Geometry of mVE

State of mVE

Neighborhood configuration

Transition rules (state of mVE)

Mesoscale Modeling

• Time dependent calculations for:

– Temperature

– Concentration

– Curvature

– Equilibrium at the S/L interface

– Crystallographic orientation -

– Growth angle -

– Growth anisotropy -

– Stochastic procedures to

control nucleation and growth

of dendrites

(t)

Liquid

Solid

n

κ

ty, x,T

ty, x,C

To Co

n

x

j

θ

θ

j

θ,f j

Columnar Dendritic Morphologies and

Segregation Patterns

Nb

Alloy 718

Dendritic Morphologies and Segregation

Patterns in Pb-10%Sn Alloy

Color Index or Sn

Dendritic Morphologies Segregation Patterns

Boundary Conditions

ESR

Ingoths

hb

hs

T(r)

VAR

h

Ingoths

hs

Radiation

heat loss Electrode

Heat flux

hb

PAM

Ingoths hs

hb

Plasma torch

Gaussian

heat flux

Radiation

heat loss

Macrostructure

Grain structure in remelt ingots (ESR alloy 718, 2 melting rates)

X X V tct t

ct

c cos R R V tc

t tct

c sin

tan 1 G

G

xm

rm

p m

n

1 1

4( )

/ 04

ta

V

2

Columnar

growth

G/V=const growth direction

probability

272 kg/hr 591 kg/hr

CET

CET in 20-inch diameter VAR alloy 718 ingots

Effect of melting rate on CET

327 kg/hr

200 kW

172 kg/hr

125 kW

Comparison of Experimental and

Simulated Grain Structure

• 20 inches diameter

• 252 kg/hr, 125 kW

Experimental Simulation (2100x2850 cells)

TL=1350 °C

Modeling of Grain Structure in ESR

Ingots

Heat Transfer Fluid FlowExperimental

Fluid Flow and Macro-segregation

patterns in ESR Alloy 718 Ingots

Nbo = 5.34 %

Diameter = 0.432 m

(17 in.)

5.0

5.1

5.2

5.3

5.4

5.5

0 50 100 150 200 250

R a dius [m m ]

Nb

[w

t. %

]

C alculated

Experim ental

Comparison of Simulated and

Experimental PAM Ti-17 Ingot–365 kg/hr

Experimental Simulated

Comparison of Predicted and Experimental Grain

Size Distributions in Ti-17 PAM Ingots

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

Ingot Radius [mm]

Gra

in S

ize

[mm

]

exp (800 lbs/hr)

exp (1200 lbs/hr)

calc (800 lbs/hr)

calc (1200 lbs/hr)

Measurement height is 0.5 m below ingot top

Dendritic Morphologies in a PAM-

Processed Ti-17 Ingot

Near ingot surface Near ingot center

Columnar and Equiaxed Grains in a PAM-

Processed Ti-17 Ingot

surface mid-radius center

Process Optimization: Melt Rate Effect on Ti-

17 PAM Ingot Macrostructures (D=0.432 m)

230 kg/hr (1x10-4 m/s)460 kg/hr (2x10-4 m/s)

Equiaxed Nucleation Rate Effects on the

Columnar Grain Size of VAR Ingots

Low equiaxed nucleation rate High equiaxed nucleation rate

Alloy 718

Macro/Microsegregation

Influence of Gravity Acceleration on Macrosegregation and Macrostructure

6.3

6.5

7

7.5

7.8

8

8.58

8

9

9.5

10

17.31916.5

15

13

11.5

10.5 10.2

9.8

10

10.02

10.05

10.1

fin

ger

sch

ann

els

po

ck

ets

freck

les

Ben

ard

cel

ls

Racr = 2000

0.01 g

• Freckles

• Pockets

• Channels

• Fingers

• Benard cells

GS=0.5mm

GS=0.1mm

Hot Topping in VAR Ingots

Start-up Constant

melting rateHot topping

Melting rate versus time in VAR

Initial

transientQuasi-steady state regime

Final

transient

With hot toppingWithout hot topping• 508 mm Diameter VAR Ingot

• Alloy 718

• Power input 125 kW

• Increase yield by 15 %

Melting Rate Effect

D = 508 mm

VAR, 172 kg/hr

D = 432 mm

ESR, 272 kg/hr

D = 432 mm

ESR, 591 kg/hrD = 508 mm

VAR, 327 kg/hr

Microstructure

Prediction of Laves and NbC phases in VAR alloy 718 (1997)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

4.5 5.0 5.5 6.0 6.5

Nb Content [wt. %]

Lav

es C

on

ten

t [w

t. %

]

C=0.02%C=0.06%

C=0.12%

C=0.09%

Ingot center

Ingot edge

Exp.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4.5 5.0 5.5 6.0 6.5

Nb Content [wt. %]

Nb

C C

on

ten

t [w

t. %

] Ingot center

Ingot edge

C=0.02%

C=0.06%

C=0.12%

C=0.09%

Exp.

0.1 mm

0.1 mm

Microstructure in VAR Alloy 718

Prediction of Laves and NbC phases in VAR alloy 718

0.1 mm 0.1 mm 0.1 mm

Exp.-Radavitch, 1997 Calc.-Laves phase Nb microsegregation

Monte Carlo Monte Carlo

wt. %

0.1 mm

Microstructure Prediction in ESR Alloy

718 Ingots

0.1 mm

Calculated Globular Laves Distribution

Experiment

0.1 mm

Calculated

Nb Microsegregation

• Grain Structure

• Nb Microsegregation

• SDAS

• Laves Distribution

0.1 mm

wt. %