Suresh G. Advani

The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites

The properties of a set of even‐order tensors, used to describe the probability distribution function of fiber orientation in suspensions and composites containing short rigid fibers, are reviewed. These tensors are related to the coefficients of a Fourier series expansion of the probability distribution function. If an n‐th‐order tensor property of a composite can be found from a linear average of a transversely isotropic tensor over the distribution function, then predicting that property only requires knowledge of the n‐th‐order orientation tensor. Equations of change for the second‐ and fourth‐order tensors are derived; these can be used to predict the orientation of fibers by flow during processing. A closure approximation is required in the equations of change. A hybrid closure approximation, combining previous linear and quadratic forms, performs best in the equations of change for planar orientation. The accuracy of closure approximations is also explored by calculating the mechanical properties o...

Melt processing and mechanical property characterization of multi-walled carbon nanotube/high density polyethylene (MWNT/HDPE) composite films

High density polyethylene (HDPE) was used as the matrix material for a carbon nanotube (CNT) polymer composites. This combination of composite constituents has not been previously reported in the literature. Multi-wall carbon nanotube (MWNT)/HDPE composite films were fabricated using the melt processing method. The composite films with 0, 1, 3 and 5% nanotube content by weight were analyzed under SEM and TEM to observe nanotube dispersion. The mechanical properties of the films were measured by small punch test. Results show increases in the stiffness, peak load and work to failure for the composite films with increasing MWNT content.

Closure approximations for three‐dimensional structure tensors

A tensor description of the orientational structure in a fiber suspension provides an efficient way to compute flow‐induced fiber orientation, but the scheme requires an accurate closure approximation for the higher‐order moments of the orientation distribution function. This paper evaluates a number of different closure approximations, comparing transient orientation calculations using the tensor equations to a full calculation of the distribution function. We propose a new hybrid closure approximation for three‐dimensional orientation, formed by modifying the scalar measure of fiber alignment. The new scheme is tested in a variety of flow fields against the commonly employed quadratic L1 and H&L2). None of these closure approximations provide accurate solutions for all the flow and orientation fields. The quadratic closure exhibits stable dynamic behavior, but predicts neither the correct transient behavior nor accurate steady‐state values, especially for nearly random to intermediately aligned orientat...

Flow of generalized Newtonian fluids across a periodic array of cylinders

Traditionally, the capillary model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the ef...

Use of epoxy/multiwalled carbon nanotubes as adhesives to join graphite fibre reinforced polymer composites

In this study, different weight fractions of multiwalled carbon nanotubes were dispersed in epoxy to produce toughened adhesives. The reinforced adhesives were used to bond the graphite fibre/epoxy composite adherends. Single lap joint samples were prepared and the average shear strengths were experimentally measured. Significant enhancement of the bonding performance was observed as the weight fraction of carbon nanotubes was increased.

Rheology of multiwall carbon nanotube suspensions

Carbon nanotubes have exhibited unusually large changes in selective physical and mechanical properties when added to polymers or polymer composites in small quantities. To understand their rheological behavior and processibility, we mixed multiwalled carbon nanotubes (MWNT) in epoxy and created suspensions of different dispersion qualities, MWNT aspect ratios, concentrations, suspension network structures, and MWNT orientation states. Their rheological properties were measured with a cone and plate rheometer. It was found that as MWNT dispersion quality improved or their network connections, the aspect ratio or concentration increased, the MWNTs interactions became stronger as indicated by a higher storage modulus G′, complex viscosity ∣η*∣, and steady shear viscosity η. It was found that suspensions which contained a mixture of separated MWNT along with small MWNT aggregates exhibited G′ that was independent of frequency suggesting solidlike behavior. This frequency sweep method could be used to charact...

On Flow through Aligned Fiber Beds and Its Application to Composites Processing

In process modeling of continuous fiber composites, matrix flow through aligned fiber beds is traditionally described by Darcys law, which relates matrix flow rate to matrix pressure gradient, matrix viscosity, and fiber bed permeability. This phenome nological relationship was originally derived for macroscopically isotropic beds of spheri cal or sphere-like particles. Hence it is necessary to establish the conditions under which this relationship may be extended to fiber beds, which are approximately transversely iso tropic. A review of previous work on steady-state Newtonian fluid flow through isotropic porous media is used as a foundation to explore the validity of extending Darcys law to flow through beds of aligned fibers. Theoretical analyses are compared to experimental results obtained from flow through real fiber beds and ideal beds of regularly spaced cylinders. Functional relationships for flow of generalized Newtonian fluids through iso tropic sphere beds are also reviewed, and their extension to aligned fiber beds is suggested as a first order approximation. The findings are discussed in terms of the usefulness and accuracy of the reviewed and suggested flow rate-pressure drop relationships in process modeling of continuous fiber composites.

EXPERIMENTAL INVESTIGATION OF TRANSVERSE FLOW THROUGH ALIGNED CYLINDERS

Abstract In this paper, flow of viscous fluids across an array of solid and porous circular cylinders, which represents a porous media, is explored experimentally. The idealized array or bed of cylinders, which models tows and fibers in a fiber preform used in composites processing, was unidirectional consisting of either solid circular rods or porous circular bundles. By measuring the flow rate and pressure drop across this bed of cylinders, we characterized the transverse permeability of the model porous media. In beds with porous bundles, the volume fraction inside the bundles ranged from 60 to 75% by packing 50–60 nylon fibers into 6.35 mm diameter holes. Both Newtonian and shear thinning fluids were used. These fluids were pumped through the medium such that the flow was perpendicular to the fiber axes. Once the fiber bed was fully saturated, the permeability was determined with the aid of Darcys law. For the solid rods, the experimental results compare well with the asymptotic model recently developed by Bruschke & Advani for generalized Newtonian fluids. In addition, a heterogeneous fiber bed was constructed, consisting of fiber bundles in a regular array. During the filling stage, the progress of the flow front through the heterogeneous fiber beds was observed and the flow-induced void formation inside the fiber bundles was monitored. None of the existing permeability models could predict the permeability of the heterogeneous porous media. A series expansion was suggested to estimate permeabilities of such heterogeneous media.

DIFFUSION-INDUCED GROWTH OF A GAS BUBBLE IN A VISCOELASTIC FLUID

The diffusion-induced growth of a spherical gas bubble surrounded by a thin shell of viscoelastic fluid containing a limited amount of dissolved gas is analyzed. This is representative of a situation when a large number of bubbles grows in close proximity in a viscoelastic medium. The upper-convected Maxwell model is employed to describe the rheology of the fluid. Limited quantities of the dissolved gas available in the liquid shell mandates solution of the convection-diffusion equation, as opposed to using similarity solutions or polynomial profiles to describe the mass transport across the interface. Utilizing the properties of a potential field and a Lagrangian transformation, a new approach is introduced to solve the coupled system of integro-differential equations governing the bubble growth. The results indicate that, at the early stages of the growth, bubbles in a viscoelastic fluid grow faster than in a Newtonian fluid. However, eventually they attain the same steady-state configuration.

The interaction between micro- and macro-scopic flow in RTM preforms

Abstract Both experimental and modeling results are presented to convey the wide span of length scales over which flow in porous media can occur in a single material. Flow in such heterogeneous porous media are shown to be important in composites processing because the structure of fibrous reinforcements contains multiple length scales. Flow phenomena that arise due to material heterogeneity have been shown to include void formation and to explain the differences observed between measurements of the ‘wet’ permeability and the ‘dry’ permeability. The work presented indicates that the heterogeneous reinforcement structure may also contribute to the differences observed in permeability measurements carried out by the radial flow and the one-dimensional flow methods. The concept of heterogeneous porous media is also extended to the molecular level by considering the flow problem in a reinforcement sized with grafted macromolecules.