MS&E Colloquium - Rollett

Date: |
September 19, 2008 from 2:00 pm to 3:00 pm EDT |

Location: |
214 S. W. Mudd |

Contact: |
For further information regarding this event, please contact Chad Gurley by sending email to cg2029@columbia.edu . |

Info: |
Click Here to Visit Website. |

**3D Digital Polycrystals
and Microstructure-Property Relationships**

A.D. Rollett, S.-B. Lee,
G.S. Rohrer, R.A. Lebensohn

Three-dimensional
polycrystal microstructures are becoming available as technologies such as
automated serial sectioning and synchrotron-based microscopy develop. Such datasets are typically images, i.e. the
local crystal orientation is defined on a regular grid of points. Interfaces between grains must then be
interpolated as surfaces between the grid points. The statistics of grain boundaries in
single-phase materials can be characterized in terms of the grain boundary
character distribution (GBCD). GBCD
means the relative frequency over the five macroscopic degrees of freedom for a
boundary, commonly parameterized by the lattice misorientation and boundary
normal. Even after a surface has been
interpolated between the grains to segment the multi-material image, smoothing
must be applied because of the stair-stepped nature of the boundaries thus
generated. Numerous methods are being
applied to this problem, of which we review one based on a moving finite
element method and one that is termed constrained line straightening that is
inspired by the methods used to find boundary segments in orientation maps. The GBCD is extracted from the information on
grain orientation and boundary normal.
Comparisons with GBCD obtained by stereological methods applied to 2D
cross sections show good agreement between the various approaches.

Once a 3D representation
has been obtained, various methods are available to calculate its
properties. For mechanical response, use
of finite element methods is standard.
Converting a 3D image into a finite element mesh is simple if one
(cubic) element per voxel is used; this, however, leads to large meshes and the
interfaces are stair-stepped. Generating
a conforming 3D mesh that follows the boundaries is a non-trivial problem that
still lacks a standardized solution. An
alternative approach is to model the mechanical properties on the image itself,
which can be done with spectral method.
Preliminary results from calculating the response under uniaxial tension
on a sample of a nickel alloy are given.
Stress concentrations and their relationship to grain boundaries are of
particular interest, for example, since they can determine the location of
rapid damage accumulation.

Acknowledgments

Support from the MRSEC
program of the NSF under Award DMR-0520425 is acknowledged. The provision of 3D datasets for IN100 by J.
Li (CMU) S. Dillon (CMU), M. Groeber (OSU) and M. Uchic (AFRL) is gratefully
acknowledged.