Short Fiber Suspensions Research Articles

Dispersibility optimization of short carbon fiber suspension for the preparation of carbon fiber aligned mat reinforced composites

There is significant interest in the reuse of reclaimed carbon fiber (rCF) due to its economic potential and the minimization of environmental impact. However, the sub-optimal state of short rCF adversely affects its reuse value. In this paper, short rCF was aligned using wet alignment technology and the dispersibility of short carbon fiber (SCF) suspension was investigated, along with virgin carbon fiber (vCF) and rCF aligned mat reinforced epoxy (EP). The results show that the main factors that affect the dispersion rate (γ) are the HEC content, CF length, CF content and ultrasonic power, in diminishing order of magnitude of impact. The HEC content was positively correlated with γ, and the CF length and CF content negatively correlated with γ. When the ultrasonic power was less than 50%, it was positively correlated with γ, and higher than 50%, it was negatively correlated. This work suggests that the dispersibility optimization of SCF suspension to obtain well aligned rCF mat offers a possible strategy to obtain an improved quality form of rCF.

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

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.

Relationship between fiber orientation and solvent viscosity for short-fiber suspension

Relationship between fiber orientation and solvent viscosity for short-fiber suspension

Learning the Macroscopic Flow Model of Short Fiber Suspensions from Fine-Scale Simulated Data.

Fiber–fiber interaction plays an important role in the evolution of fiber orientation in semi-concentrated suspensions. Flow induced orientation in short-fiber reinforced composites determines the anisotropic properties of manufactured parts and consequently their performances. In the case of dilute suspensions, the orientation evolution can be accurately described by using the Jeffery model; however, as soon as the fiber concentration increases, fiber–fiber interactions cannot be ignored anymore and the final orientation state strongly depends on the modeling of those interactions. First modeling frameworks described these interactions from a diffusion mechanism; however, it was necessary to consider richer descriptions (anisotropic diffusion, etc.) to address experimental observations. Even if different proposals were considered, none of them seem general and accurate enough. In this paper we do not address a new proposal of a fiber interaction model, but a data-driven methodology able to enrich existing models from data, that in our case comes from a direct numerical simulation of well resolved microscopic physics.

From elastic homogenization to upscaling of non-Newtonian fluid flows in porous media

Upscaling behaviors of heterogeneous microstructures to define macroscopic effective media is of major interest in many areas of computational mechanics, in particular those related to materials and processes engineering. In this paper, we explore the possibility of defining a macroscopic behavior manifold from microscopic calculations, and then use it directly for efficiently performing manifold-based simulations at the macroscopic scale. We consider in this work upscaling of non-Newtonian flows in porous media, and more particularly the ones involving short-fibre suspensions.

Orientation kinematics of short fibres in a second-order viscoelastic fluid

Most theoretical fibre suspension models currently used for predicting the flow-induced evolution of microstructure in the processing of reinforced thermoplastics are based on the Jeffery model of dilute suspensions in a Newtonian suspending fluid or phenomenological adaptations of it that account for fibre-fibre interactions. An important assumption of all these models is the Newtonian character of the fluid in which the fibres are suspended. In industrial practice, the considered fluids are in general molten thermoplastics that exhibit a viscoelastic behaviour. Even though few counterparts of the Jeffery theory exist for second-order fluids, they have been rarely considered and, to our knowledge, never taken into account at the macroscopic scale. In this paper, we address the modelling of short fibre suspensions in second-order fluids throughout the different description scales, from microscopic to macroscopic. We propose a simplified modelling framework that allows one to extend to viscoelastic suspending fluids the standard Folgar and Tucker model widely used in industrial simulation software.

The shear viscosity of carbon fibre suspension and its application for fibre length measurement

The viscosity of short carbon fibre suspensions in glycerol aqueous solution was measured using a bespoke vane-in-cup viscometer, where the carbon fibre has an aspect ratio from 450 to 2209. In the semi-concentrated regime, nL 3 ranging from 20 to 4400, the suspensions demonstrated strong shear-thinning characteristics particularly at higher concentrations. The shear-thinning characteristic is strongly related to the crowding factor proposed by Kerekes, indicating that non-hydrodynamic interactions occur in the suspensions. The influence of fibre bending on viscosity emerges when the bending ratio is lower than 0.0028. An empirical model based on transient network formation and rupture was proposed and used to correlate the relative viscosity with fibre concentration nL 3 and shear rate. Based on the model, a viscosity method is established to analyse the fibre length by measuring the viscosity of the fibre suspension using a bespoke vane-in-cup viscometer.

A study on fiber sedimentation velocity in epoxy/steel fiber composites used for hybrid injection molds

Composites based on metallic fibers and thermosetting polymers are being increasingly used for molding blocks of hybrid injection molds, thereby improving the mechanical and thermal properties. However, an adequate study on the behavior of steel fibers in a reactive epoxy resin is necessary to understand how to maintain suitable mold properties. In this paper, the sedimentation velocity of short steel fiber suspensions in reactive epoxy resin was estimated using a model emerging from the Stokes equation and considering the resin rheology and correction factors for the fiber shape and concentration. DMP (2,4,6-tris (dimethylamino-methyl) phenol) was the accelerator more suitable for this type of composites because it increases the rate of cure and reduces the gel time more pronouncedly than any of the other common accelerators. Samples were manufactured with epoxy resin, short steel fiber and DMP as accelerator, and using anti-sedimentation equipment. The distribution of the fibers was observed in all composites. The viscosity data were used to predict the time in the anti-sedimentation equipment necessary to reach a minimum sedimentation velocity using the mathematical model. Results showed that this velocity is recommended to be below 3.28 × 10−8 m/s to avoid sedimentation of the steel fibers.

Simulation of flow of short fiber suspensions through a planar contraction

In this study, the flow of a fiber filled viscoelastic matrix through planar contractions is investigated. It was found that by adding fiber to the matrix vortex, the intensity increases. Fiber orientation along “x” and “y” axes was studied too. It was found that fiber orientation could be used for determining the flow regime through the contraction geometry. The rigidity condition of fibers, which needs the trace of the orientation tensor to be unity everywhere in the domain, is correct except near walls and the reentrant corner, which is slightly less than one. In these regions, the stress magnitude is higher, which results in more numerical errors, and which further leads to some error in predicting the orientation tensor. The first normal stress difference distribution along different axes was also studied in this article. It was found that increasing the volume concentration of fibers results in first normal stress difference intensification.

Rheology and processing of suspensions with fiber, disk and magnetic particles

This paper introduces recent development and progress in rheology and processing of suspension materials. In particular, three topics with different suspensions will be discussed, which are relevant in polymer- and powder-based manufacturing industries for various applications. The paper begins with a fundamental study of rheological modeling for short fiber suspension in a viscoelastic liquid. Irreversible thermodynamics based approach is presented to describe the polymer viscoelastic deformation with the fiber anisotropy effect taken into account. Several distinguishing features of the model are presented. Then we turn our attention to more industry-oriented subject of pigment disk orientation in injection molding of aesthetic plastic parts. The major difference between fiber and disk orientation kinematics is briefly discussed using Jeffery model. Experimental and numerical results for the disk orientation and the surface color of the molded part are presented. Finally, we introduce our recent efforts regarding the rheology of magnetic particle suspension, which is an essential part for a development of precision magnetic powder injection molding process. Some rheometer data for stainless steel powder suspensions are presented.

Irreversible thermodynamics based constitutive theory for fiber suspended polymeric liquids

A rheological model for a short fiber suspension in polymeric liquid is proposed according to irreversible thermodynamics of viscoelastic deformation of polymers with the effect of fiber orientation taken into account. In this model, the evolution of elastic deformation tensor, namely, reversible Finger strain tensor, is governed by not only the reversible Finger strain tensor but also the fiber orientation tensor in a manner of a positive entropy production. The final form of stress tensor combines the viscoelasticity of polymeric matrix of the Leonov model and the fiber contribution of the Dinh–Armstrong model. The Folgar–Tucker model is employed for fiber orientation kinematics along with an invariant-based optimal fitting closure approximation. The rheological behavior of the model is comprehensively studied using steady and transient shear flows.

Modeling the behavior of fiber suspensions in the molding of polymer composites

Mechanistic simulations of fiber suspensions to predict final fiber orientation distribution in the molding of fiber-reinforced composites have been developed. The mathematical algorithm models fibers as chains of connected rigid beads. Parameters such as fiber volume fraction, number of beads per fiber, and fiber flexibility can be modified to model diverse processing conditions. This article focuses on the extensional flow of short fiber suspensions at high fiber concentrations. Simulation results were compared with predictions obtained with the Folgar—Tucker model. It was found that for the case of short fiber suspensions, fiber orientation is well predicted by the Folgar—Tucker model with the interaction constant CI in close agreement with a model proposed by Phan-Thien et al. It was also found that fiber—matrix separation increases with the increase of fiber aspect ratio. The mathematical model presented in this study provides a tool to predict defects and to model orientation distribution in the processing of fiber-reinforced composites.

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s − 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.

Fiber orientation kinetics of a concentrated short glass fiber suspension in startup of simple shear flow

The common approach for simulating the evolution of fiber orientation during flow in concentrated suspensions is to use an empirically modified form of Jeffery's equation referred to as the Folgar–Tucker (F-T) model. Direct measurements of fiber orientation were performed in the startup of shear flow for a 30 wt% short glass fiber-filled polybutylene terephthalate (PBT-30); a matrix that behaves similar to a Newtonian fluid. Comparison between predictions based on the F-T model and the experimental fiber orientation show that the model over predicts the rate of fiber reorientation. Rheological measurements of the stress growth functions show that the stress overshoot phenomenon approaches a steady state at a similar strain as the fiber microstructure, at roughly 50 units. However, fiber orientation measurements suggest that a steady state is not reached as the fiber orientation continues to slowly evolve, even up to 200 strain units. The addition of a “slip” parameter to the F-T model improved the model predictions of the fiber orientation and rheological stress growth functions.

Obtaining reliable transient rheological data on concentrated short fiber suspensions using a rotational rheometer

The conventional method for obtaining transient rheological data on short glass fiber-filled polymeric fluids is to use the parallel disk (PP) geometry in a rotational rheometer. Using the PP geometry large transient stress overshoot behavior was observed during the startup of flow measurements on a 30 wt % short glass fiber-filled polybutylene terephthalate. A contributing factor to this behavior is believed to be induced fiber collisions caused by the inhomogeneous velocity field (radial varying velocity gradient). A novel approach was taken in which a “donut” shaped sample was used in a cone-and-plate device (CP-D) to maintain a sufficient gap to fiber length ratio. The magnitude of the first normal stress difference was reduced by 70%, and the time to reach steady state was reduced by 100 strain units. The Lipscomb model coupled with the Folgar–Tucker model for the evolution of fiber orientation was fit to the stress growth behavior measured using both the PP geometry and CP-D resulting in different parameters. In addition, the fitted model parameters were found to depend on the initial fiber orientation. It is believed that the CP-D allows for an accurate determination of the stress growth behavior and eventually will allow one to obtain unambiguous model parameters.

Modeling fibre orientation in short fibre suspensions using the neural network-based orthotropic closure

Industrial methods for modeling the fibre orientation within short-fibre reinforced polymer composites require the use of a closure approximation, whereby the equation of motion for an even-ordered orientation tensor depends on the next higher even-ordered orientation tensor. The orientation within the processed part correlates to the material stiffness tensor; therefore it is essential to have confidence in the accuracy of the selected closure. This paper suggests a novel methodology in formulating a closure by employing an artificial neural network (ANN) training algorithm, and presents the coordinate frame invariant Neural Network-Based Orthotropic Closure (NNORT). Results demonstrate that, for most of the flows investigated, the NNORT closure offers accuracies representing the orientation and the stiffness tensors, equal to or greater than the current industrially employed closures, without any computational increases.

Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows.

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.

An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence

Recent experiments suggest that short fibers in concentrated suspensions align more slowly as a function of strain than models based on Jeffery’s equation predict. We develop an objective model that captures the slow orientation kinetics exhibited by short-fiber suspensions. The standard moment-tensor equation of fiber orientation is used to find equations for the change rates of the eigenvalues and eigenvectors of the orientation tensor. As a phenomenological assumption, the growth rates of the eigenvalues are reduced by a constant scalar factor, while the rotation rate expressions for the eigenvectors are unchanged. The eigenvalue/eigenvector equations are then reassembled as a tensor equation. An equivalent kinetic theory is also developed. The new model is tested in a variety of flows, and found to exhibit slower kinetics than the standard model but similar steady-state orientations. The model provides an excellent fit to the shear stress transient in a shear reversal experiment with a 30% glass fiber filled polybutylene terephthalate resin melt, and we show how this experiment can be used to determine the parameters of the model.

Flow-driven orientation dynamics of semiflexible fiber systems

We study the flow-induced orientation dynamics of semiflexible fibers in dilute fiber suspensions. Starting from the equations of motion for a two-rod model of flexible fibers in Stokes flow, the Smoluchowski equation for a connected monomer orientation distribution function is derived. We then obtain a set of equations for the time dependence of the first and second moments of the orientation distribution function, thus extending the Folgar Tucker equations for short rigid fiber suspensions to flexible fiber suspensions. The resulting generalized equations for the orientation dynamics of a suspension of flexible fibers are solved for simple channel flow. It is shown that all qualitative effects of bending and straightening of fibers and their influence on the orientation of flexible fibers are captured within our model. A scalar measure for the distribution of bending in a flow is introduced, which allows to detect the degree of bending of fibers.