Gas Transport in Out of Autoclave Processing of the Prepregs

In AC processing, the high compaction pressures generate high resin pressure and consequently reduced void size or dissolution of gaseous species in the resin. In OOA processing, the main means of void reduction is reducing the pressure of the gasses inside the voids. Gas removal is necessary but not sufficient for void reduction as some of the void spaces are rigid (surrounded with fiber or semi-solid resin) and once evacuated, they need to be compacted and/or filled with resin before the system gels. Gas evacuation can occur through diffusion or advection

mechanisms.

2.2.2.1 Diffusion

Diffusion is the molecular movement of species in the bulk of the material, under concentration gradients. Fick’s first law of diffusion is written as [40]

𝐽 = −𝐷^𝑑𝐶_𝑑𝑥 (2-2)

Where 𝐽 (kg/m²s): diffusion mass flux, 𝐷 (m²/s): diffusion coefficient, 𝐶 (kg/m³): concentration and 𝑥 (m): distance.

Moisture is known as one of the primary sources of voids in OOA prepregs [3, 7, 41]. Void growth can happen through diffusion of moisture from the resin into a void [19, 20]. Researchers have investigated air and moisture diffusion in epoxy prepregs and have developed models that predict void growth and collapse via diffusion based on processing parameters such as pressure and temperature [7, 35, 42, 43]. Kardos model is the most commonly cited diffusion based void growth model [35]. Kardos model predicts the effect of resin moisture content on the void diameter [7, 35]. In this model it is assumed that a spherical void is located in an infinite

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isotropic resin medium and its growth happens through water diffusion from the surrounding resin [7, 35]. Using this model the evolution of isolated resin voids through diffusion can be predicted.

Where d: void diameter (mm), β: growth driving force, D: diffusion coefficient of water in the resin (mm²/hr), t: time (hr), Cbulk: concentration of water in the bulk resin (gr/mm³), Cvoid: concentration of water at the surface of the void (gr/mm³), ρg: gas density (gr/mm³).

2.2.2.2 Advection

Advection is another means of gas transport, which refers to continuum or bulk flow of gas. Gas advection in porous medium is widely analyzed using Darcy’s law [44], which states that the superficial gas velocity (v) is directly proportional to the gas permeability of the porous medium and the pressure gradient of gas phase in the direction of the flow. In one dimension, this can be expressed by

𝑣 = −^𝐾_𝜇^𝑑𝑃_𝑑𝑥 (2-5)

Where 𝐾 (m²): gas permeability, µ (Pa.s): gas dynamic viscosity, P (Pa): gas pressure, 𝑥 (m):

distance.

Darcy’s law is applicable to laminar flow. The Reynolds number (Re) determines the boundary between turbulent and laminar flow regimes. The transition from laminar to turbulent flow

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regime is determined by Reynolds number (Re) and occurs in the range of 1 to 10 [45]. In low pressure or low permeability medium there is a transition from laminar flow to Knudsen diffusion or free molecular flow. Gas advection in porous medium can be thought of as flow through many capillary tubes. In the case of large capillary tubes, the mean free path for gas molecules is much smaller than tube radius and thus continuum flow occurs. As the size of the capillaries gets smaller and close to the gas molecular mean free path, free molecule or Knudsen diffusion occurs [44]. Knudsen showed that at low pressures, the mass flux reaches a minimum and then increases as the pressure decreases. This increase is a result of free molecular flow or slip phenomenon in which the gas velocity is not zero at the wall [44]. This effect is also known as the Klinkenberg effect [44].

A prerequisite for advective or Darcy flow in a porous medium is the presence of a continuous network through which the bulk movement of gas can occur. A partially impregnated prepreg is a porous medium that has a complex microstructure which changes during the process. This porous network consists of both connected and isolated void spaces that are surrounded with resin and fibers. Darcy flow occurs through the interconnected network of voids as long as they are open and not filled with resin. The pressure inside the interconnected network of voids can be reduced via Darcy flow and vacuum application, whereas the pressure inside isolated voids can only change through gas diffusion mechanisms, under constant void volume conditions. The interconnected porosity network in prepreg laminates consists of their un-impregnated zones called Engineered Vacuum Channels (EVACs) [23, 28, 29]. The morphology of the EVACs change throughout the process, as they become infiltrated with heated low viscosity resin.

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2.2.2.2.1 Permeability

Permeability quantifies the porous medium resistance to advective flow and depends on

geometrical characteristics such as porosity, surface area and tortuosity [46]. Permeability is not measured directly, it is calculated based on an assumed flow model and measured flow related data (e.g., flow rate, pressure) [44]. For this reason, permeability measurements have meaning only in the context they are measured. This is why permeabilities measured for different flow geometries or different scales may give different values [44, 47]. Below, some of the available methods for measurement of air permeation in porous medium are reviewed.

Permeability is determined by application of pressure gradient across a porous medium and measurement of the resultant air flux. Air permeability in porous medium has been extensively studied in the fields of soil science, oil and gas extraction and filtration. Both steady and non-steady state methods are employed. The non-non-steady state or pressure decay method is commonly used for low permeability materials where steady-state flow condition can not be achieved in a reasonable time. The steady state method is commonly used in laboratory settings. In this test a steady state gas flow (Q) is produced by applying a constant pressure gradient across the sample.

Permeability, K, is determined by solving the one dimensional Darcy flow equation for a compressible ideal gas at constant temperature [34, 46]

𝐾 = ^{2𝜇𝐿𝑄}_𝐴 ¹_𝑃 ^𝑃1

12− 𝑃₀² (2-6)

Where µ: gas viscosity, L: length of the sample, A: cross sectional area of the sample, P₁: the inlet pressure, P0: outlet pressure.

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The porous medium in prepregs is fibrous in nature. An important characteristic that

distinguishes fibrous porous medium from granular medium is their relatively high porosity.

Fibers form stable structures with high specific surface area and with relatively low resistance to flow [48]. However, in the case of prepregs the fibrous structure is partially impregnated with resin and during the cure cycle the porous structure changes as resin infiltrates into it which in turn affects the permeability of the laminate.

Prepreg gas permeability has been studied in the past [10, 11, 49, 50, 51]. Through-thickness permeability of prepregs was measured based on falling pressure technique by Tavares et al.

[51]. In-plane and through thickness permeability at ambient and heated conditions was

measured by Arafath et al. [34] with a steady-state experimental set-up based on work by Seferis et al. [50]. Studies have shown that gas permeability is anisotropic and generally significantly greater in in-plane compared to through-thickness at ambient conditions for prepregs that are created by applying a resin film to the surface of the dry fibres [11, 53, 54].