To view this presentation:

  • If you have an MRS account, click the Login button above.
  • New to MRS?  Create a free account here



  0       0

2014 MRS Fall Meeting


NN1.01 - A Theory and Challenges for Coarsening in Microstructure


Dec 1, 2014 8:30am ‐ Dec 1, 2014 9:00am

Description

Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such simplicity emerge from such complexity?

Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution. The properties of the evolving network that characterize the GBCD must be identified and appropriately upscaled or 'coarse-grained'. This entails identifying the evolution of the statistic in terms of the recently discovered Monge-Kantorovich-Wasserstein implicit scheme. The undetermined diffusion coefficient or temperature parameter is found by means of a convex optimization problem reminiscent of large deviation theory.

Joint work with K. Barmak (Columbia), M. Emelianenko (George Mason). Y. Epshteyn (Utah), R. Sharp (Globys), and S. Ta'asan (CMU)

Speaker(s):

You must be logged in and own this session in order to post comments.

Print Certificate
Review Answers
Print Transcript
Completed on: token-completed_on
Review Answers
Please select the appropriate credit type:
/
test_id: 
credits: 
completed on: 
rendered in: 
* - Indicates answer is required.
token-content

token-speaker-name
token-index
token-content
token-index
token-content
token-index
token-content
token-index
token-content
token-index
token-content
token-index
token-content
/
/
token-index
token-content
token-index
token-content