Fitting FiveParameter Grain Boundary Character in 3D Digital Microstructures

1
Fitting Five-Parameter Grain Boundary Character
in 3D Digital Microstructures

• Lisa Chan
• Carnegie Mellon University
• Dr. Anthony Rollett Dr. Gregory Rohrer

2
Motivation

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

Gertsman et al., Acta Mater., 49 (9) 1589-1598
(2001).
2
3
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).
3
4
Five Parameter Grain Boundary Character
Distribution
three Euler angles
4
Modified from Saylors TMS 2002 slide
5
Plan
target grain boundary character distribution
target orientation distribution
digital microstructure
Simulated Annealing
output orientation distribution grain boundary
character distribution
5
6
Microstructure Builder
1512 grains
2D.M. Saylor et al., Metall. Mater. Trans. A 35A
(7) 1969-1979 (2004).
6
7
Rolling Texture Rolled Copper
Rolled copper data obtained from Dr. Samuel Lim
8
Experimental GBCD
9
Flowchart of Algorithm
Simulated Annealing
output orientation distribution grain boundary
character distribution
10
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
11
Simulated Annealing
Weighting Values
where
Probability of accepting evolution step
T annealing temperature
12
Annealing Temperature
T
13
Flowchart of Algorithm
Simulated Annealing
14
Future Work

• create more statistically representative
  microstructures
• perform more simulations to analyze the effects
  of texture strength and grain geometries on grain
  boundary character distribution

14
15
Thank You
16
Stereology for measuring GBCD
The probability that the correct plane is in the
zone is 1. The probability that all planes are
sampled is lt 1.
D.M. Saylor et al., Metall. Mater. Trans., 35A
1981-1989 (2004).