Mechanical Engineering Commons^™

Heterogeneous Anisotropy Index And Scaling In Multiphase Random Polycrystals, Muhammad Ridwan Murshed

Theses and Dissertations

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 …