The investigation of the constraints imposed by the distributions of orientations and boundary norma

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The investigation of the constraints imposed by
the distributions of orientations and boundary
normals in sample space on the grain boundary
character distribution
Thesis Overview

• By Lisa Chan
• Advisor Dr. Anthony Rollett and Dr. Gregory
  Rohrer

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Outline
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Motivation

• Grain Boundary Engineering (GBE) consists of
  repeated cycles of deformation annealing, to
  generate large fractions of special boundaries
  and avoid strong recrystallization textures.

Palumbo et al., JOM., 50 2 40-43 (1998).
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Motivation

• Several ?3 boundaries with larger deviations
  from ideal misorientation cracked.

Gertsman et al., Acta Mater., 49 (9) 1589-1598
(2001).
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Motivation

• Cracked ?3 boundaries were found to deviate more
  than 5from the trace of the 111 plane.

Lin et al., Acta Metall. Mater., 41 (2) 553-562
(1993).
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Scientific Questions

• What are the limits on generating realistic
  microstructures and grain boundary character
  distribution based on given characteristics?
• If fixed with grain shape and texture, can we
  still optimize the distribution of CSL
  boundaries?

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Hypothesis
Hypothesis The grain boundary character
distribution is constrained by the grain
orientations and grain boundary plane
orientations in sample space (grain shapes).
For example, it is not possible to obtain
populations of a specific boundary type with a
three-dimensional equiaxed polycrystalline
microstructure, and texture strength greater than
5.
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Microstructure Generation
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• Microstructure Generation
• Synthetic Microstructures
• Microstructure Builder
• Plank Generator
• Voronoi Tessellation
• FIB-Reconstructed Structures
• Twin Insertion

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Microstructure Builder
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Microstructure Builder
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Plank Generator
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Voronoi Tessellation
Step 2. Segment volume such that each cell
contains only 1 point
Tetrakaidecahedron-shaped grains
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Tetrakaidecahedrons
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FIB-reconstructed Structures
Zirconia obtained from Dr. Shen Dillon, and
Inconel 100 obtained from Dr. Michael Groeber
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Twin Insertion

• Pick random grain
• Identify orientation of grain
• Rotate 111 vector from crystal to sample
  reference frame
• Use equation of plane
• D distance from center (range 0-1)

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Twin Insertion

• Tolerance controls thickness of twin

Tolerance (twin width) 0.5 Tolerance (
twin width) 3
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Crystallography Generation
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• Crystallography Generation
• Fiber Texture
• Random Texture
• Rolling Texture
• CSL Misorientations

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Fiber Texture
Probability density distribution for normal
distribution
where ? mean ? standard deviation
Garbacz et al., Acta Metall. Mater., 412
475-483 (1993).
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Fiber Texture
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Random Texture
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Rolling Texture Rolled Copper
Rolled copper data obtained from Dr. Samuel Lim
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OD and MD of Rolled Copper
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CSL Misorientations
?3
?1, 3, 7
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Orientation Assignment
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• Orientation Assignment
• Simulated Annealing Algorithm
• Validation of Algorithm

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Simulated Annealing
(1) Assign an orientation to each grain
(2) Simulated annealing minimization1
Approach a configuration that minimizes error
1Miodownik et al., Acta Mater., 47 (9) 2661-2668
(1999).
Saylors TMS 2002 slide
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Simulated Annealing
Weighting Values
or
where
R v - 1
2
Probability of accepting evolution step
T annealing temperature
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Weighting Values
Inputs
odf_weighting 0mdf_weighting 2
odf_weighting 0.67mdf_weighting 0.22
odf_weighting 1.82mdf_weighting 0.031
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Weighting Values
RMS ODF difference RMS MDF difference
best MD fit
Log scale
best OD fit
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Weighting Values
best OD and MD fit
RMS ODF difference RMS MDF difference
constant total error
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Weighting Values
best linear fit
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Validation of Algorithm
Garbacz et al., Scr. Mater., 23 (8) 1369-1374
(1989). Gertsman et al., Acta Metall. Mater., 42
(6) 1785-1804 (1994). Morawiec et. al., Acta
Metall. Mater., 41 (10) 2825-2832 (1993). Pan et
al., Scr. Metall. Mater., 30 (8) 1055-1060
(1994).
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Results

• Results
• Geometrical Effects on MD
• Number of Grains
• Grain Size Distribution
• Grain Shapes
• Effects of OD on MD

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Number of Grains
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Grain Size Distribution
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Grain Size Distribution
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Grain Shapes
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Effects of OD on MD
Most compatible OD and MD
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Summary
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Research Plan
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Research Plan

• Twin Insertion Algorithm
• maintain texture of material
• match twin cluster statistics observed
  experimentally
• match distribution of twins per parent grain
• match twin width distributions
• Grain Shape Analysis
• quantify grain shapes in current structures with
  mean width
• create structures with specific mean widths
• Improve GBCD Algorithm
• use performance analysis tools such as Shark and
  Tau
• parallelization of the algorithm such that more
  CPUs are used to calculate GBCD
• obtain additional GBCDs for exploration on the
  limitations OD and grain shape has
• on the GBCD

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Questions
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Supplemental Slides
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Simulated Annealing
ODF Error
Error
1/Temperature
Possible ODF
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Simulated Annealing

• Randomly populate Representative Volume
  Element (RVE) OD in homochoric space
• Sample RVE OD from step (1) to select
  2000xN representative orientations
  (N number of specific 2000 grain
  RVEs used)
• Randomly assign orientations to each grain of
  each RVE
• Perform internal simulated annealing loop to
  shuffle orientations so that the MD of each RVE
  matches the specified MD
• Compute error as sum of error from all models,
  automatically accept if error is lower or compute
  probability of acceptance if error is higher
• Accept if delt0 or random numberltexp(-de/t)
• Randomly perturb OD bins, reduce temp of
  simulation and repeat

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Simulated Annealing Temperature
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Simulated Annealing Temperature
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Simulated Annealing Temperature
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Twin Cluster
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Random Texture Components
Values in volume percent ()
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Pole Figure for Random Texture
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Experimental GBCD
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Title
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