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