Multi-scale characterization of orthotropic microstructures

Abstract

Computer-generated 2D microstructures of varying second phase area fraction (5–30%), aspect ratio (1–16) and degree of alignment (where the reinforcement major-axis orientation is random, perfectly aligned or semi-aligned) are analyzed via the isotropic and directional forms of the computationally efficient multi-scale analysis of area fractions (MSAAF) technique. The impact of these microstructure parameters on the representative volume element (RVE) necessary to characterize a microstructure is ascertained with variations in isotropic and directional homogeneous length scales, derivative quantities of the MSAAF technique. Analysis of these results produces empirical expressions for the directional homogeneous length scale as a function of area fraction and aspect ratio for the limiting cases of random and 'perfect' second phase alignment. Generally, particle alignment is observed to increase the aspect ratio of a microstructure's RVE—a trend amplified by higher reinforcement aspect ratios and lower area fractions. Particle alignment also decreases the absolute size of such an element by reducing the directional homogeneous length scales transverse to the axis of alignment. Periodic boundary conditions on the perimeter of the synthetic microstructures are used to characterize the error in the MSAAF technique via multiple instantiations of the same microstructure, which further indicates that the statistical variation in the directional homogeneous length scale (measured by the directional MSAAF technique) can be an order of magnitude less than the variation in the isotropic homogeneous length scale (measured by the isotropic MSAAF technique).