Modelling Rapid Solidification Kinetics Quantitatively using Phase field Models

Transcript

1. Modelling Rapid Solidification Kinetics
   Quantitatively using Phase field Models
   Nikolas Provatas
   McGill University, Department of Physics
   Centre for the Physics of Materials
   Spring Meeting, Sept 26-27, 2021
   

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2. “Phase Field crystal“ (PFC)
   10-10 10-8 10-6 10-4 10-2 100
   Length Scale (m)
   104
   102
   100
   10-2
   10-4
   10-6
   10-8
   10-10
   10-12
   Time Scale (s)
   FEM
   Atomic potentials MD/DFT/MC
   Atomic kinetics
   Phase Field (PF)
   Heat
   Transfer
   Casting
   Solidification
   Time and Length Scales of Materials Phenomena
   Precipitation
   Grain
   boundaries
   Solute trapping
   Solute diffusion
   Dendritic
   solidification
   

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3. Large-scale heat transfer
   Alloy design
   Microstructure design
   Melt pool flow
   Process design
   Computational
   thermodynamics
   Property and performance design
   Phase field method
   Micromechanics and crystal plasticity
   Integration of Phase Field Simulations with Integrated computational
   materials engineering (ICME)
   Powder
   manufacturing
   Microstructure
   imaging, XRD, EDS
   Nanoindentation, fatigue and
   corrosion testing, …
   Rapid solidification tests,
   process monitoring, AM DoEs
   Partnership with VTT Technical Research Centre of Finland
   

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4. Phase Field Modelling of Solidification
   

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5. Multi-Phase & Multi-Component Solidification
   ➢ Chemical potentials:
   ➢ One order parameter for each grain/phase:
   ➢ Concentrations in each phase :
   ➢ Grand potential of each phase :
   ➢ Local atomic mobility:
   ➢ Susceptibility tensor of each phase:
   ➢ Local susceptibility:
   Greenwood et al, 2018, Comp. Mat. Sci. 142
   

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6. Parabolic Free Energy Approximation
   J.Heulens, B. Blanpain and N. Moelans
   Acta Materialia, 59 (2011)
   Database Calc Parabolic fitting
   

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7. Quantitative Contact with Solidification
   Benchmarks formulated for Dilute Binary Alloys
   steady state concentration sharp interface limit
   

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8. Simulating Across Multiple Scales
   

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9. W
   1mm
   40mm
   130mm
   Color map represents
   impurity concentration (C)
   ~102 -103nm
   Dendrite Spacing » L
   Interface Width » w
   capillary length = d
   o
   dendrite radius = r
   Length Scale Selection in Directional Solidification
   [2D: M. Greenwood et al, Phys. Rev. Lett, Vol. 93, 246101 (2004)
   3D: Provatas et. Al, Int. J. Mod. Phys. Vol. 19, 4525 (2005)]
   

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10. domain
    subdomain
    subdomain
    mini-mesh →finite difference
    3D Adaptive Mesh Refinement (AMR): Architecture
    Oct -tree in 3D
    [M. Greenwood, et. al J. Com. Mat. Sci. Vol. 142, 153 (2018)]
    

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11. Scalability Across Distributed Processors
    

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12. Scalability Across Distributed Processors
    equivalent uniform mesh nodes=
    system dimensions:
    128 dendrites
    each dendrite occupies ~32 domains, spread over 8 cores
    # or cores= 8 X dendrites in system
    

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13. Scalability Across Distributed Processors
    8
    16
    32
    64
    512
    1024
    8
    16
    32
    64
    512
    1024
    128
    twall
    =time of one dendrite simulated alone,
    in one core
    twall
    =time of full simulation domain
    Y-axis→
    X-axis→
    

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14. View Slide

15. https://www.eos.info/additive_manufacturing/for_technology_interested
    Application: Metal Laser Sintering of Al-Si-Mg
    In Collaboration with Mohsen Mohammadi and
    Hossein Azizi @ Marine Additive Manufacturing
    Centre of Excellence University of New Brunswick
    

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16. Single-layer powder base metal system (X-Z plane) at t=0
    7
    Result
    8.0e+00
    4
    3 6
    .0e-04 2
    1 5
    400 $m
    Powder
    40 $m
    Base
    X
    Y
    X
    Z
    &'
    &(
    &)
    1.9e+03
    1800
    1600
    Field_30
    800
    1200
    1.9e+03
    1800
    1400
    1000
    Horizontal
    X
    Y
    X
    Z
    P
    Vertical
    Laser direction
    P
    X
    Y
    Unsteady Heat Transfer in Semi-infinite So
    Solidification process of the coating layer during a ther
    operation is an unsteady heat transfer problem. As we d
    earlier, thermal spray process deposits thin layer of coat
    materials on surface for protection and thermal resistant
    as shown. The heated, molten materials will attach to th
    and cool down rapidly. The cooling process is importan
    the accumulation of residual thermal stresses in the coa
    solid
    liquid
    Coating with density ,
    latent heat of fusion: hsf
    Substrate, k,
    Centerline
    1600
    Field_30
    1200
    1.9e+03
    1800
    1400
    1000
    Horizontal
    X
    Y
    X
    Z
    P
    Vertical
    Laser direction
    P
    X
    Y
    Unsteady Heat Transfer in Semi-infinite Solids
    Solidification process of the coating layer during a thermal spray
    operation is an unsteady heat transfer problem. As we discuss
    earlier, thermal spray process deposits thin layer of coating
    materials on surface for protection and thermal resistant purposes
    as shown. The heated, molten materials will attach to the substra
    and cool down rapidly. The cooling process is important to preve
    the accumulation of residual thermal stresses in the coating layer.
    S(t)
    solid
    liquid
    Coating with density ,
    latent heat of fusion: hsf
    Substrate, k,
    Centerline
    Initial temperature profiles of the cross section of the melt pool (X-Z plane)
    1.9e+03
    1600
    Field_30
    1200
    1.9e+03
    1800
    1400
    1000
    Horizontal
    X
    Y
    X
    Z
    P
    Vertical
    Laser direction
    P
    X
    Y
    Unsteady Heat Transfer in Semi-infinite Solids
    Solidification process of the coating layer during a thermal spray
    operation is an unsteady heat transfer problem. As we discuss
    earlier, thermal spray process deposits thin layer of coating
    materials on surface for protection and thermal resistant purposes,
    as shown. The heated, molten materials will attach to the substrate
    and cool down rapidly. The cooling process is important to prevent
    the accumulation of residual thermal stresses in the coating layer.
    S(t)
    solid
    liquid
    Coating with density ,
    latent heat of fusion: hsf
    Substrate, k,
    Centerline
    Case Study in Dilute Al-Si System:
    FEM Modelling of Thermal Transfer Conditions
    

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17. 1.1e+00
    0.5
    t =5.0
    t =8.0
    X
    X
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    B B
    C
    A A
    A
    A
    B
    Increasing nucleation density
    × 10$ %s
    1.1e+00
    0.5
    t =5.0
    t =8.0
    X
    X
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    B B
    C
    A A
    A
    A
    B
    Increasing nucleation density
    × 10$ %s
    t = 0.5 ms
    1.1e+00
    0.5
    t =5.0
    t =8.0
    X
    Y
    X
    Z
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    B B
    C
    A A
    A
    A
    B
    Increasing nucleation density
    × 10$ %s
    t = 0.8 ms
    Microstructure Evolution in Horizontal Build Sample
    

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18. Microstructure of the fully solidified layer: Horizontal VS. Vertical
    Build Directions
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    t =5.0
    t =8.0
    X
    Y
    X
    Z
    B B (c)
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    B B
    C
    A A
    A
    A
    B
    Increasing nucleation density
    × 10$ %s
    1.1e+00
    0.5
    t =5
    t =8
    X
    Y
    X
    Z
    9 2e-03
    0.02
    Field_4
    0.1
    0.2
    1.1e+00
    0.5
    0.05
    B B
    C
    A A
    A
    A
    B
    Increasing nucleation density
    × 10
    

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19. Modelling Non-Equilibrium Interfacial
    Kinetics in Rapid Solidification
    

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20. ➢Example: consider model C
    ➢Can make contact with the sharp interface model
    even when the interface and
    21
    Sharp Interface Limit of Basic “Model C”
    phi-4 potential Tilts the wells
    /
    M
    p
    T T
    u
    L c
    −
    =
    l ≪1
    

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21. Separation of Length Scales
    (solid)
    f field
    -
    f = -1
    Phase-field model solutions
    U field
    Sharp-Interface phases
    interface
    Outer region
    Outer region
    Inner region
    Classic approach: phase-field (order parameter) and
    temperature field approach sharp-interface profiles
    when →0
    f =1
    (liquid)
    -d
    o
    k -bV
    n
    Sharp-Interface U=(T-Tm
    )/Tm
    Outer region
    

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22. Scaling Relations
    ➢ In the limit of: and
    Second order in
    perturbation theory
    Capillary length
    Interface kinetic coefficient
    Matching inner and
    outer regions
    

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23. Quantitative Phase Field Modeling of Solute Trapping and
    Continuous Growth Kinetics for Rapid Solidification
    • Most phase field models emulate sharp interface limit where
    k(V) = ke
    • Solute trapping should affect
    1. Solute partitioning k(V) > ke
    2. Kinetic undercooling (generalized Gibbs-Thomson condition)
    • Using matched asymptotic boundary layer analysis , we
    incorporate solute trapping into the phase field model with
    the following:
    1. Controllable k(V) which is [relatively] independent of the chosen
    interface width W
    2. Follows kinetic undercooling according to Continuous Growth
    Model (CGM) kinetics with either full or zero solute drag
    

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24. Continuous Growth Model Description (CGM)
    • Popular sharp interface model for solute trapping
    • Kinetic undercooling depends on k(V) as follows:
    = 1 gives complete solute drag, and = 0 gives zero solute drag
    Goal: Want phase field model to follow CGM undercooling (1) and to
    approximate a k(V) curve
    Approach: Use sharp interface asymptotics by modifying the so-called ”anti-
    trapping” current
    M. J. Aziz and W. J.Boettinger, Acta Metall. Mater. 42 (1994)
    

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25. Setting Up Phase Field Model for SIM Analysis
    

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26. Recovering the CGM k(V) in the Sharp Interface Limit
    Anti-trapping form→
    Modify anti-trapping coefficient →
    →full drag
    →no drag
    Modified CGM-SIM coefficients
    A controls solute trapping →
    ( k(V) made independent of W by keeping A*W constant)
    binary alloy
    

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27. Model Convergence
    Kinetic
    undercooling
    Tatu Pinomaa and Nikolas Provatas, Acta Materialia, Vol. 168, 167 (2019)
    

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28. In-situ imaging of rapid solidification
    Dynamic transmission electron microscopy (DTEM)
    Copper concentration (EDXS) STEM image quality map Inverse polar
    figure map
    McKeown, Joseph T., et al. "Time-resolved in situ measurements during rapid alloy solidification:
    Experimental insight for additive manufacturing." JOM 68.3 (2016): 985-999.
    • Explicit (in-situ) imaging of rapid solidification
    • Controlled conditions (~ 2D, no flow, simple heat transfer)
    • Crucial for calibrating and validating solidification models
    Application: Rapid Solidification of Aluminum Alloys
    Collaboration with Tatu Pinomaa and Ansi Laukkanen (VTT) & Jörg M.K. Wiezorek and Joseph T. McKeown (Laurence Livermore National Labs)
    

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29. • No latent heat release
    • T-independent material
    properties
    • Heat transfer 2D
    Modelling Thermal Transfer Conditions
    

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30. 21/07/2022 VTT – beyond the obvious 31
    Phase field modeling DTEM
    

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