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 .
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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.