Application of the Spectral Methods of Microstructure Design to Continuous Fiber-reinforced Composites

Abstract

A new mathematical framework called microstructure-sensitive design (MSD) has recently been developed to facilitate solutions to inverse problems in microstructure design, where the goal is to identify the complete set of relevant microstructures that are theoretically predicted to satisfy a set of designer-specified criteria on effective properties or performance. This methodology has been applied previously to a few design-related case studies, mainly involving polycrystalline metals. This article describes the first application of MSD methodology to customized design of continuous fiber-reinforced composites for specified combinations of performance criteria. The main contribution of this study is that it presents a novel but simple mathematical framework for the application of first-order MSD to the design problems involving continuous fiber-reinforced composites. In the examples presented in this article, elementary first-order theories spanning two length scales have been selected to obtain effective properties of continuous fiber-reinforced composite material systems. Having selected these first-order theories, the authors proceed to demonstrate the viability of applying the first-order MSD framework to design the case studies in continuous fiber-reinforced composites.

Statistical methods for mechanical characterization of randomly reinforced media

“…Spectral methods, incorporating microstructural correlation functions, use spectral representations of distribution functions that statistically characterize the internal structure of representative volumes and connect these representations and macroscale effective properties using existing homogenization schemes (Kalidindi and Houskamp 2007).…”

Spectral methods for microstructure design

“…Limited explorations have also been conducted into compositional variations in microstructures 10 and into fiber-reinforced composites. 11 In cubic and hexagonal polycrystalline metals, the MSD framework has been successfully applied to a few design case studies. These have included maximizing the deflection in a compliant beam, 12 maximizing the in-plane load-carrying capacity of a thin plate with a central circular hole, 10 and minimizing the elastic driving force for crack extension in rotating disks.…”

Microstructure metrics for quantitative assessment of particle size and dispersion: Application to metal-matrix composites

“…MSD can predict mechanical properties while featuring invertible linkages between the statistical description of a microstructure and its effective properties [1,2]. The framework was largely focused on the statistical description of crystal orientations using orientation distribution functions (ODFs) as the primary metric for microstructures [1][2][3][4][5]. This paper presents an extension of the previously developed microstructure metrics for quantitative description of microstructures in the statistical sense to enable assessment of particle size and dispersion in metal-matrix composites (MMCs).…”