Assessment of Analytical Orientation Prediction Models for Suspensions Containing Fibers and Spheres

Bastien Dietemann,Fatih Bosna,Torsten Kraft,Claas Bierwisch,Harald Kruggel-Emden

doi:10.3390/jcs5040107

Abstract

Analytical orientation models like the Folgar Tucker (FT) model are widely applied to predict the orientation of suspended non-spherical particles. The accuracy of these models depends on empirical model parameters. In this work, we assess how well analytical orientation models can predict the orientation of suspensions not only consisting of fibers but also of an additional second particle type in the shape of disks, which are varied in size and filling fraction. We mainly focus on the FT model, and we also compare its accuracy to more complex models like Reduced-Strain Closure model (RSC), Moldflow Rotational Diffusion model (MRD), and Anisotropic Rotary Diffusion model (ARD). In our work, we address the following questions. First, can the FT model predict the orientation of suspensions despite the additional particle phase affecting the rotation of the fibers? Second, is it possible to formulate an expression for the sole Folgar Tucker model parameter that is based on the suspension composition? Third, is there an advantage to choose more complex orientation prediction models that require the adjustment of additional model parameters?

Highlights

IntroductionMechanical properties of fiber-reinforced engineering materials often depend on their local orientation of fibers [1,2]
While the governing equation of the Folgar Tucker (FT) model is precisely described, its implementation allows a certain degree of freedom when it comes to the closure approximation
The simulations are performed in 2D, and the default formulation applied in this work is the 2D formulation of the FT model in combination with the hybrid closure approximation if not stated differently

Summary

Introduction

Mechanical properties of fiber-reinforced engineering materials often depend on their local orientation of fibers [1,2]. Specimens are reported to be stronger in the direction of fiber alignment [3], or the alignment of the fibers influences the thermal conductivity in sheet layers [4]. There is a desire to predict the orientation for a specific process to optimize a part with respect to a specific mechanical property. The problem set up for investigation is illustrated, which shows an exemplary extrusion process in which a paste filled with fibers and spheres is extruded through a nozzle. The final orientation of the fibers in the extruded filament is complex to predict as it arises from an interplay of experienced hydrodynamic forces and interactions between the particles during the printing process

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