Phase Field Models of Ternary Eutectoid Alloys (Presentation 1)

Almambet Iskakov, Robert Pienta

12 00 AM ,Mon, Sep 14 2015

Background

• Directional Solidification of Al, Ag, Cu Eutectic Alloy
• Control structure during solidification process
• Align phases/structures parallel to growth direction
• Achieve desired material properties

Phase-Field Simulation: Solidification

• Solidification Model:
  • Simulate growth of phases
  • Thermodynamic model
  • Concentration model
  • Three phase metal
  • Varied Parameters: Temperature Gradient and Gradient Velocity

Directional Solidification Visual

Phases evolve parallel to growth direction.

Binary Phase Diagram

• Eutectic mixture:
  • Liquid transforms into two different phases
  • Lowest melting/freezing temperature

• In this Al, Ag, Cu alloy, the eutectic ratios by mole fraction at 773.6K:
  • 18% Ag (25% experimental)
  • 69% Al (62% experimental)
  • 13% Cu (14% experimental)

Simulated Microtstructure

• A cross-section of solidified material close to solidification front
• Most continuous phase: Al
• Chained brick-like structure: Al₂Cu and Ag₂Al

Common Microstructure Patterns

The Data

• More than 20 simulations
  • Resolution from 200x200 to over 2000x2000
  • Simulated with varied solidification velocities
  • Varied volume-fractions of Al, Ag₂Al, and Al₂Cu
  • Plenty of measurements!
    • An 800x800x4256 sample has 2.72 billion data points
      • This simulation took 16 hours on 13700 cores!

Simulation in action

Al = Green, Ag₂Al = Orange, and Al₂Cu = Blue

Extracting Features

We have already started generating spatial statistics (correlations) for our data

0 = Al, 1 = Ag₂Al, and 3 = Al₂Cu

Distance-varying Distributions

• The simulated microstructures vary through the course of each simulation
• We can sample the approximate steady-state, solidified structure at various times,
  • using the difference between successive spatial statistics
  • or just using one of the last time/height steps (assuming that the simulation was run until a steady state was reached)
• We may later consider the changes in spatial statistics over time to help mine the Process-Structure linkages

Computational Plans

Next Steps

• Use dimensionality reduction (DR) over our large space of spatial statistics:
  • Conventional PCA
  • Newer low-rank approximation DR techniques
  • (possibly) Attempt to use locality sensitive hashing

• Model the relationship between our simulated solidification processes
  • linear model (regression)
    • interpretable
    • simple model, unlikely that Eutectoid Al has linear structural relationships
  • nonlinear model (kernel methods)
    • less interpretable
    • complex model, can model complex relationships

Questions & Comments

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