Correlation structure in the elasticity tensor for short fiber-reinforced composites

TL;DR

This paper analyzes the mesoscale material properties and correlation structure of the elasticity tensor in short fiber-reinforced composites, combining analytical and numerical methods to account for fiber geometry variability.

Contribution

It provides a combined analytical and numerical approach to study the correlation structure of the elasticity tensor considering probabilistic fiber geometry in SFRC.

Findings

Correlation functions differ between plane strain and plane stress states.

Numerical results validate analytical calculations.

Material behavior is confirmed as transversely-isotropic.

Abstract

The present work provides a profound analytical and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.