Study of Concentrated Short Fiber Suspensions in Flows, Using Topological Data Analysis.

Rabih Mezher,Francisco Chinesta,Jack Arayro,Nicolas Hascoet

doi:10.3390/e23091229

Abstract

The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the flow induced orientation, on the fibers’ geometrical center trajectory. The number of interactions as well as the interaction intensity will depend on the fiber volume fraction and the applied shear, which should affect the stochastic trajectory. Topological data analysis (TDA) will be applied on the geometrical center trajectories of the simulated fiber to prove that a characteristic pattern can be extracted depending on the flow conditions (concentration and shear rate). This work proves that TDA allows capturing and extracting from the so-called persistence image, a pattern that characterizes the dependence of the fiber trajectory on the flow kinematics and the suspension concentration. Such a pattern could be used for classification and modeling purposes, in rheology or during processing monitoring.

Highlights

Reinforced polymers are widely used in industry for enhancing mechanical and functional performances while keeping the cost reasonable
The main issue related to the use of fiber-based reinforced polymers for elaborating short fiber composites is due to the difficulty of accurately predicting the flow induced orientation, with the final properties becoming strongly dependent on the final orientation state of fibers in the formed part
The analysis of those erratic trajectories that the fiber follow, should provide a very valuable information on the orientation state, the local concentration that could differ from one point to another in the flow, or even the effective velocity gradient that could differ from the nominal one, that as previously indicated is assumed the one unperturbed by the fibers presence

Summary

Introduction

Reinforced polymers are widely used in industry for enhancing mechanical and functional performances while keeping the cost reasonable. When considering a description based on the orientation tensors (orientation distribution moments), the diffusion term describing fiber interaction within the Folgar & Tucker formulation, results in a sort of randomizing term that tends, to evolve the orientation towards the isotropic state, that is a → I/3 (in 3D), with I the identity tensor [2,4]. It is postulated that this trajectory will depend on the number and intensity of the fiber interaction, both expected scaling with the flow gradient of velocity, the fiber concentration and the orientation state. The analysis of those erratic trajectories that the fiber follow, should provide a very valuable information on the orientation state (difficult to measure in 3D flows of concentrated suspensions), the local concentration that could differ from one point to another in the flow, or even the effective velocity gradient that could differ from the nominal one, that as previously indicated is assumed the one unperturbed by the fibers presence.

Discrete Simulation

Fiber Motion Equations

Topological Data Analysis

Results

Conclusions