O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Recent Advances in Modeling of Solidification Behavior J. M. Vitek 1, S. S. Babu 2 and S.

OAK RIDGE NATIONAL LABORATORY

U. S. DEPARTMENT OF ENERGY

Recent Advances in Modeling of Solidification Behavior

J. M. Vitek1, S. S. Babu2 and S. A. David1

1 Oak Ridge National Laboratory2 formerly ORNL, now at Edison Welding Institute

Presented at Trends 2005

Pine Mountain, Georgia

May 16 to 20, 2005



Acknowledgements• This research was sponsored by the programs

within the U. S. Department of Energy, under contract DE-AC05-00OR22725 with UT-Battelle, LLC:– Division of Materials Sciences and Engineering– Advanced Turbine Systems Program, Office of Fossil

Energy– NNSA Initiatives for Proliferation Prevention Program

• The authors would also like to thank General Electric Corporation for providing the Rene N5 alloy.



Understanding Weld Solidification is Critical

• Solidification behavior determines weldability and solidification structure controls properties and performance

• Weld solidification is related to casting but it has many unique features– High growth rates, cooling rates and thermal

gradients– Vigorous fluid flow– Epitaxial growth– Conditions that vary with position



Modeling Provides the Path Toward Understanding Weld

Solidification Behavior



Outline

• What I will cover:– Thermodynamic, kinetic and phase

transformation modeling applied to solidification– Interface response functions– Welded single crystal grain structures– Phase field modeling

• What I won’t cover– Heat and fluid flow modeling

• Recurring theme: integration of models



I. Computational Thermodynamics: The Backbone of Advanced Models• Need to know the phase

diagram (phase stability for multicomponent systems and as a function of temperature)

• Need to identify solute redistribution

• Computational thermodynamics (CT) addresses all of these



Solidification Involves:• Competition among primary phases• Stabilization of non-equilibrium phases as a

result of segregation• Non-equilibrium solidification temperature

ranges, often well beyond equilibrium ΔT• Solute redistribution, strongly affected by

solidification morphology, and vice versa• Solidification structure and solute distribution

that influence solid-state transformations, in-service behavior, stability, etc

CT provides the basis for quantifying all of these



CT Has Advanced Significantly in the Last 10 Years

• Many more systems are covered, including specialty databases

• Thermodynamic databases are more accurate

• CT can be used extensively in IRF models, phase field models, etc



What Can Be Done with CT?



Ex 1:Sample Scheil

Simulations

• For IN718 alloy

• To 99% solid

• Routines also available for partial inclusion of solid state diffusion



Ex 2: Diffusion Kinetics Models Interface with CT

• Include:– Solid state diffusion– Scaling effects– Undercooling

• Classic application is to interdendritic segregation

L



But Diffusion Kinetics Models Can Be Used for Much More

• Consider Al-4 wt % Cu system

• 10 µm cell size• Consider only primary

FCC solidification• Follow profiles versus

time

L

time

L



Interdendritic Effects Can Be Examined

• Standard dendrite theory considers only isolated dendrite

• Can model dendrite shape

• Between dendrites have undercooling and segregation which may lead to:– New dendrites– New grains– New phases



Dendrite Shape and Interdendritic Undercooling in Al-4Cu

solid

liquid

Arbitrary thermal gradient (1.3 x 106 K/m) was used and this determines vertical length

μm

μm



Example 3: Kinetics Calculations Explain FN Distribution in Castings

• FN distribution in 316SS can’t be explained by:– Solidification mode change– Intuitive solid-state

transformation behavior• Combined with thermal

profiles, kinetics calculations solve problem

Low FN

High FN



FN Distribution Is a Combination of

Solidification and Solid State Cooling

Rates

Edge

Center



II: Interface Response Functions

• IRF calculates growth front undercooling as a function of solidification phase and its morphology– Non-equilibrium effects are taken into account

• IRF identifies solidification phase (when competition is possible) and solidification morphology (planar front, dendritic)

Based on work of Kurz and co-workers.



In-Situ Experiments Showed a Solidification Mode Change in Fe-Mn-C-Al

to Austenite Solidification at High Solid-Liquid Interface Velocities

Co

oli

ng

arc-off

Background

Maximum Intensity



TRXRD Measurements Conclusively Confirmed Equilibrium -Ferrite Solidification

Mode at Lower Cooling Rates

• This is confirmation that switching occurs as a function of interface velocity.

Co

oli

ng

Slope-start

arc-off

IRF Calculations for Fe-C-Al-Mn Agree with Experiment Only If Parameters Are Changed

• Calculations depend on–kv, Partition coefficient = f{Velocity, Temperature}–mV, Liquidus slope = f{Velocity,Temperature}–R, Dendrite tip radius = f{kv,mv}–Cl*, Interface concentration = f{kv}–Gibbs Thompson coefficient



• Single crystals represent a technologically important class of materials

• Successful welding of single crystals, yielding crack-free single crystal welds, is needed

• Modeling of solidification behavior in single crystals is needed to understand and advance this technology– Modeling has identified mechanism of stray

grain formation

III: Solidification Grain Structure in Welded Single Crystals



200µmFe-15Cr-15Ni: perfect, no stray grains

Ni superalloy: lots of stray grains and cracks

Avoiding Stray Grains Is the Key to Welding Single Crystals



Proper Evaluation Must Combine Several Sub-Models

• Heat and fluid flow to identify weld pool shape and solidification conditions along weld pool (thermal gradient, solidification front velocity)

• Geometrical model identifies active base metal dendrite growth direction as a function of solidification front orientation

• Nucleation and growth model identifies tendency to form new (stray) grains

Schematic of problem and contribution of each model

• Heat and fluid flow model– ID weld pool shape

– ID thermal gradients

– ID growth velocity as f(weld speed)

• Geometric model– Relate dendrite orientation to

solidification front

– Relate dendrite growth velocity to solidification front velocity

• Nucleation and growth model– Relate formation of new grains ahead of

SF to undercooling ahead of dendrites



Theory for Extent of Constitutional Supercooling Has Been Derived by Gäumann et al

n

30

n

1n

1

]1ln[3

N4a

V

G

G = thermal gradientV = growth velocityN0 = nucleation rateΦ = stray grain volume fractiona, n = material constants

Φ was calculated over the entire weld pool since V, G vary; it was calculated for many different weld powers, speeds, and crystallographic orientations

3

n/1n0

)aV/G)(1n(

1

3

N4S

where

Se1or



Calculations Predict Stray Grain Formation Tendencies

• Find range of probabilities over entire pool

• Find effect of weld conditions on tendencies

Tendency to Form Stray Grains as a Function of Location Was Found

Blue = low likelihood of stray grains, Red = high likelihood of stray grains.

Asymmetric, low speedSymmetric, low speedSymmetric, high speed



The Optimum Weld Processing Conditions Could Be Identified

4000

3000

2000

1000

0

Pow

er (

W)

4 5 6 7 8 90.01

2 3 4 5 6 7 8 90.1

2 3 4 5

Weld Speed (ms-1

)

0.5

0.5

0.4

5 0.45

0.4

0.4 0.35

0.35

0.3

0.3

0.25 0.2

0.2 0.15

0.1

[110], (001) Orientation

4000

3000

2000

1000

0

Pow

er (

W)

4 5 6 7 8 90.01

2 3 4 5 6 7 8 90.1

2 3 4 5

Weld Speed (ms-1

)

0.5

0.5 0.4

5

0.4

0.4 0.35 0.3 0.25 0.2 0.15 0.1


4000

3000

2000

1000

0

Pow

er (

W)

4 5 6 7 8 90.01

2 3 4 5 6 7 8 90.1

2 3 4 5

Weld Speed (ms-1

)

0.5 0.4

5

0.45

0.4

0.4 0.35 0.3

0.25

0.2

0.2

0.15

0.1


Low power and high speed yield the lowest predicted values of Φ



IV: Phase Field Modeling Offers Many New Possibilities

• Phase field modeling is a mathematical formulism that allows for the solution of many difficult but important problems

• Phases, compositions, grain orientations are described with diffuse boundaries

• Phase transformations, grain growth, recrystallization can all be modeled

• Integration with CT provides solid basis for considering multi-component, multi-phase systems



Advantages and Disadvantages of Phase Field Modeling

Advantages

- Multidimensional

- Can handle multi-component systems with slow and fast diffusers

- Models spatial distribution

Disadvantages

- Computationally intensive

- Need to identify critical parameters- Anisotropy- Surface energy- Nucleation density,

etc



Commercial Software (MICRESS) Is Available and Was Used

• Fe- 1 at % C- 1 at % Mn

• System parameters– 0.75 x 1.5 mm size– Cooling rate of 10K/s– Thermal gradient of 25 K/mm

• Primary BCC (5 grains); nucleation of FCC (15 nuclei)

• BCC anisotropic; FCC isotropic



Solidification Movie

• Shown:– Development of dendritic structure– DAS spacing– Accommodation of secondary arms– Interdendritic nucleation of secondary FCC– Overtaking of dendrites by secondary (FCC) phase

• Could extend to:– Stray grain formation– Growth behavior as function of dendrite orientation– Phase competition



Phase Field Calculations

Provide Important Additional

Information



Phase Field Fills in the Gaps

• Adds dimensionality to kinetics (Dictra is 1D)• Adds multi-phase and directly includes

thermodynamics• Describes morphology and distribution, not

just amounts of phases (as CT and Dictra)• Could extend to look at stability in service –

how non-equilibrium phases and solute segregation will evolve during high T exposure



But Phase Field Has Problems

• Parameters may not be known very well– Nucleation rate, nucleation conditions– Anisotropy and orientation dependence of

parameters (surface energy, etc)

• Computational time– Movie took 60 hours of CPU– But parallel operations are near– Problem will diminish with time



Summary• Key components of quite sophisticated

models are available• Integration is the key• See model integration more and more;

advances will be in terms of added sophistication of component models

• Problem of identifying parameters, their reasonable values, and determining sensitivity to accuracy of parameters

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Recent Advances in Modeling of Solidification Behavior J. M. Vitek 1, S. S. Babu 2 and S.

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