$30 off During Our Annual Pro Sale. View Details »

Modelling Rapid Solidification Kinetics Quantitatively using Phase field Models

Modelling Rapid Solidification Kinetics Quantitatively using Phase field Models

Daniel Wheeler

July 21, 2022
Tweet

More Decks by Daniel Wheeler

Other Decks in Science

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

    View Slide

  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

    View Slide

  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

    View Slide

  4. Phase Field Modelling of Solidification

    View Slide

  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

    View Slide

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

    View Slide

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

    View Slide

  8. Simulating Across Multiple Scales

    View Slide

  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)]

    View Slide

  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)]

    View Slide

  11. Scalability Across Distributed Processors

    View Slide

  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

    View Slide

  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→

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  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

    View Slide

  19. Modelling Non-Equilibrium Interfacial
    Kinetics in Rapid Solidification

    View Slide

  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

    View Slide

  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

    View Slide

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

    View Slide

  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

    View Slide

  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)

    View Slide

  25. Setting Up Phase Field Model for SIM Analysis

    View Slide

  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

    View Slide

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

    View Slide

  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)

    View Slide

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

    View Slide

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

    View Slide