Percolation and homogenization theories for heterogeneous materials

Most materials produced by Nature and by human beings are heterogeneous. They contain domains of different states, structures, compositions, or material phases. How these different domains are distributed in space, or in other words, how they connect to one another, determines their macroscopic properties to a large degree, making the simple rule-of-mixtures ineffective in most cases. This thesis studies the macroscopic effective diffusion, diffusional creep, and elastic properties of heterogeneous grain boundary networks and composite solids, both theoretically and numerically, and explores the microstructure-property correlations focusing on the effects of microstructural connectivity (topology). We have found that the effects of connectivity can be effectively captured by a percolation threshold, a case-specific volume fraction at which the macroscopic effective property undergoes a critical transition, and a set of critical scaling exponents, which also reflect the universality class that the property belongs to. Using these percolation quantities together with the generalized effective medium theory, we are able to directly predict the effective diffusivity and effective diffusional creep viscosity of heterogeneous grain boundary networks to a fairly accurate degree. Diffusion in composite solids exhibits different percolation threshold and scaling behaviors due to interconnectivity at both edges and corners. Continuum elasticity suffers from this complexity as well, in addition to the complicating factor that each phase is always characterized by several independent elastic constants. These issues are each addressed in detail. In addition to studying all the above properties for a random distribution of grain boundaries or phases, we have also studied the effects of correlations in spatial distributions.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Materials Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Chen, Ying, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Christopher A. Schuh.

• Materials Science and Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/44389

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/44389