Date Approved

12-8-2017

Embargo Period

3-7-2018

Document Type

Dissertation

Degree Name

PhD Engineering (Doctor of Philosophy in Engineering)

Department

Mechanical Engineering

College

Henry M. Rowan College of Engineering

Advisor

Ranganathan, Shivakumar I.

Committee Member 1

Kadlowec, Jennifer A.

Committee Member 2

Breitzman, Anthony F.

Keywords

Heterogeneous Anisotropy Index, Mesoscale, Scaling Function, Universal Anisotropy Index

Subject(s)

Polycrystals--Elastic properties; Multiscale modeling

Disciplines

Applied Mathematics | Materials Science and Engineering | Mechanical Engineering

Abstract

Under consideration is the finite-size scaling of elastic properties in single and two-phase random polycrystals with individual grains belonging to any crystal class (from cubic to triclinic). These polycrystals are generated by Voronoi tessellations with varying grain sizes and volume fractions. By employing variational principles in elasticity, we introduce the notion of a 'Heterogeneous Anisotropy Index' and investigate its role in the scaling of elastic properties at finite mesoscales. The index turns out to be a function of 43 variables, 21 independent components for each phase and the volume fraction of either phase. Furthermore, the relationship between Heterogeneous Anisotropy Index and the Universal Anisotropy Index is established for special cases. Rigorous scale-dependent bounds are then obtained by setting up and solving Dirichlet and Neumann type boundary value problems consistent with the Hill-Mandel homogenization condition. This leads to the concept of a dimensionless elastic scaling function which takes a power-law form in terms of Heterogeneous Anisotropy Index and mesoscale. Based on the scaling function, a material scaling diagram is constructed using which one can estimate the number of grains required for homogenization. It is demonstrated that the scaling function quantifies the departure of a random medium from a homogeneous continuum.

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