Flow-induced anisotropic viscosity in short FRPs

Róbert Bertóti,Thomas Böhlke

doi:10.1186/s40759-016-0016-7

Abstract

BackgroundThe commonly used flow models for Fiber Reinforced Polymers (FRPs) often neglect the flow-induced anisotropy of the suspension, but with increasing fiber volume fraction, this plays an important role. There exist already some models which count on this effect. They are, however, phenomenological and need a fitted model parameter. In this paper, a micromechanically-based constitutive law is proposed which considers the flow-induced anisotropic viscosity of the fiber suspension.MethodsThe introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber suspension which depends on the actual fiber orientation distribution. Assuming incompressible material behaviour, a homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described based on Jeffery’s equation. The reorientation of the fibers is modeled in two ways: by describing them with fiber orientation vectors, and by fiber orientation tensors. A numerical implementation of the introduced model is applied to representative flow modes.ResultsThe predicted effective stress values depending on the actual fiber orientation distribution through the anisotropic viscosity are analyzed in transient and stationary flow cases. In the case of the assumed incompressibility, they show similar effective viscous material behaviour as the results obtained by the use of the Dinh-Armstrong constitutive law.ConclusionsThe introduced model is a possible way to describe the flow-induced anisotropic viscosity of a fluid-fiber suspension based on the mean field theory.

Highlights

The commonly used flow models for Fiber Reinforced Polymers (FRPs) often neglect the flow-induced anisotropy of the suspension, but with increasing fiber volume fraction, this plays an important role
A mean field theory based effective linear viscosity model is introduced for short fiber reinforced polymers based on a two-step homogenization method
The presented model can handle arbitrary anisotropy of the effective viscosity which is caused by the evolving orientation distribution of the fibers

Summary

Introduction

The commonly used flow models for Fiber Reinforced Polymers (FRPs) often neglect the flow-induced anisotropy of the suspension, but with increasing fiber volume fraction, this plays an important role. There exist already some models which count on this effect. A micromechanically-based constitutive law is proposed which considers the flow-induced anisotropic viscosity of the fiber suspension. The orientation distribution of discontinuous fibers in a composite has a considerable impact on the mechanical properties of the reinforced material. Polymer-composites containing short fiber reinforcements are often produced through injection molding. With the compression molding technology discontinuous long fiber reinforced polymer parts can be produced. The motivation of this work is to set up a micromechanically-based rheological model which can describe the flow-induced effective anisotropic viscous. All of them are already implemented in commercial software packages

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