Recent Advances in Modeling of Solidification Behavior

1
Recent Advances in Modeling of Solidification
Behavior

• J. M. Vitek1, S. S. Babu2 and S. A. David1
• 1 Oak Ridge National Laboratory
• 2 formerly ORNL, now at Edison Welding Institute
• Presented at Trends 2005
• Pine Mountain, Georgia
• May 16 to 20, 2005

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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.

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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

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Modeling Provides the Path Toward Understanding
Weld Solidification Behavior
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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 wont cover
• Heat and fluid flow modeling
• Recurring theme integration of models

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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

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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 ?T
• 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
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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

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What Can Be Done with CT?
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Ex 1Sample Scheil Simulations

• For IN718 alloy
• To 99 solid
• Routines also available for partial inclusion of
  solid state diffusion

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Ex 2 Diffusion Kinetics Models Interface with CT

• Include
• Solid state diffusion
• Scaling effects
• Undercooling
• Classic application is to interdendritic
  segregation

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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
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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

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Dendrite Shape and Interdendritic Undercooling in
Al-4Cu
liquid
solid
µm
µm
Arbitrary thermal gradient (1.3 x 106 K/m) was
used and this determines vertical length
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Example 3 Kinetics Calculations Explain FN
Distribution in Castings

• FN distribution in 316SS cant be explained by
• Solidification mode change
• Intuitive solid-state transformation behavior
• Combined with thermal profiles, kinetics
  calculations solve problem

High FN
Low FN
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FN Distribution Is a Combination of
Solidification and Solid State Cooling Rates
Center
Edge
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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.
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In-Situ Experiments Showed a Solidification Mode
Change in Fe-Mn-C-Al to Austenite Solidification
at High Solid-Liquid Interface Velocities
Background
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TRXRD Measurements Conclusively Confirmed
Equilibrium d-Ferrite Solidification Mode at
Lower Cooling Rates

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

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

• Calculations depend on
• kv, Partition coefficient fVelocity,
  Temperature
• mV, Liquidus slope fVelocity,Temperature
• R, Dendrite tip radius fkv,mv
• Cl, Interface concentration fkv
• Gibbs Thompson coefficient

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III Solidification Grain Structure in Welded
Single Crystals

• 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

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Avoiding Stray Grains Is the Key to Welding
Single Crystals
Fe-15Cr-15Ni perfect, no stray grains
Ni superalloy lots of stray grains and cracks
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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

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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

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Theory for Extent of Constitutional Supercooling
Has Been Derived by Gäumann et al
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Calculations Predict Stray Grain Formation
Tendencies

• Find range of probabilities over entire pool
• Find effect of weld conditions on tendencies

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Tendency to Form Stray Grains as a Function of
Location Was Found
Symmetric, high speed
Symmetric, low speed
Asymmetric, low speed
Blue low likelihood of stray grains, Red high
likelihood of stray grains.
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The Optimum Weld Processing Conditions Could Be
Identified
Low power and high speed yield the lowest
predicted values of F
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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

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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

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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

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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

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Phase Field Calculations Provide Important
Additional Information
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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

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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

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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