Center for Composite Materials - University of Delaware

Research Summary

Parametric Study of Fiber Tow Wetting by Finite Volume of Resin

Authors: Michael Yeager and Dr. Suresh G. Advani


• The main objective of this project is to optimize the performance of composite materials in extreme dynamic environments
• Energy is dissipated in continuous fiber composite materials through friction at the fiber – matrix and fiber-fiber interface, fiber-matrix debonding, and matrix deformation
• The ability to control parameters effecting the resin fill and distribution within a fiber tow allows one to optimize the contact area between the fibers and matrix
• A key goal is to identify the role and influence of material, geometric and process parameters on the impregnation of a fiber tow from a finite measured volume of resin
• In this study a model is used to investigate the effect of final static contact angle, slip length, fiber volume fraction, resin viscosity, and fiber surface roughness on the fiber-matrix interfacial area and the time it takes to infuse a unit volume containing fibers
-Fibers are usually packed in a triangular, square or hexagonal arrangement


Model Overview
• The numerical model, created in COMSOL, studies the spreading of a finite volume of resin in a unit cell containing fibers
• The resin initially begins in contact with the top fiber to alleviate the complexity associated with the impact problem

• Stokes flow – inertial forces are neglected
• Constant properties and derivatives in z-direction
• Resin does not cure during spreading, making viscosity constant
• Fibers are rigid

Governing Equations [1]

Navier-Stokes (reduced for Stokes flow)
• ρ∙u_t=-∇∙p+μ∇^2 u+ρg+F_st
Where Fst is the force from surface tension

Continuity equation
• ∇∙u=0

Level set variable, ϕ, is given by
• ϕ_t+u∙∇ϕ=γ∇∙(ε∇ϕ-ϕ(1-ϕ) ∇ϕ/|∇ϕ| )
• Where γ is the reinitialization parameter for the interface, ε is the interface thickness, and ϕ is the level set variable, which continuously changes from 0 to 1 across the interface

Density and viscosity across the interface given by
• ρ=ρ_Resin+(ρ_Air-ρ_Resin )ϕ
• μ=μ_Resin+(μ_Air-μ_Resin )ϕ

Sample Results with a fiber volume fraction of 0.55


• Wetting, the ability of a solid’s surface to stay in contact with a liquid, is quantified by the static contact angle (θ) between the solid and liquid where the static contact angle is given by
• The non-dimensional contact area is defined as the fiber-resin contact area at time t divided by the final fiber-resin contact area
• A kink occurs in the fiber-resin contact area versus time curve when the resin contacts the bottom fiber because at that time the resin gains an additional surface to spread on
• For decreasing final static contact angles, the kink generally occurs at lower times due stronger forces driving the wetting of the fibers
• Higher contact angles resulted in a smaller fiber-matrix contact area due to a lower affinity for the resin to wet the fibers


• The slip condition at the wetting wall is quantified through use of a slip length (β), described in the figure above [1]
• The slip length did not have an impact on the final resin distribution within the unit cell
• Increasing the slip length showed a significant impact on the amount of time it took for the resin to wet the fibers
• The sensitivity of wetting rate to slip length was enhanced as the slip length approached zero


• For increasing volume fraction, the kink in the fiber-resin contact area versus time curve generally occurs at lower times due to the bottom fiber being closer to the top fiber
• This does not hold with very high fiber volume fractions because the gap between fibers is so small that it impedes resin flow
• Packing the fibers tighter increases the contact area between the fibers and resin, but only significantly until a limit
• This limit would increase if the fiber diameter was smaller, a larger volume of resin was used, or if the final static contact angle between the fibers and resin was decreased


• Viscosity did not impact the final distribution of the resin within the unit cell
• Viscosity had a linear impact on the rate at which the resin covered the fibers
• N% Contact area signifies that the resin has wetted N% of the final fiber-resin contact area


• Before making the 3D model required to investigate the impact of surface roughness, a simple 2D study using a model of resin spreading on a plate with sinusoidal surface roughness is used to investigate the role of surface roughness
• Results show that with that for surface roughness of up to 150 nm, there is not a significant impact on wetting
• The S2 Glass fiber surface roughness, measured using an AFM, was on the order of 10 nanometers, indicating that surface roughness will not have a significant effect on wetting


• The final contact area significantly impacted the final fiber-matrix contact area and the rate of wetting
• The resin viscosity linearly effected the rate of wetting
• The slip length, tailored by changing the fiber sizing, had a large effect on the wetting rate
• Fiber surface roughness, within a reasonable average value, was found to be negligible
• Fiber volume fraction played a large role in wetting and appeared to allow an avenue for fiber-matrix contact area optimization


[1] COMSOL Multiphysics Reference Manual Version 4.4. Nov. 2013.


Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

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