Experimental study of dynamic air permeability for woven fabrics

Abstract

Dynamic permeability is relevant to textile applications subjected to fluid/gas flow under high pressure, such as automotive airbags, wearable airbags and parachute fabrics. Dynamic permeability can be determined when a porous medium is tested under transient pressure conditions. This paper utilizes a reliable approach to measure and characterize dynamic permeability for woven fabrics. The experimental principle is based on the ideal gas law and the non-linear Forchheimer equation. Compared with static permeability measured under a constant low pressure, the dynamic permeability is an intrinsic property determined by change of fabric geometry and structure due to a high-pressure load. The pressure-induced deformation is identified, including effects on fiber and yarn arrangement, yarn porosity and fabric thickness. The level of deformation is a function of the number of fabric layers and initial pressure drop. The experimental results show that the dynamic permeability is higher than the static permeability for loose fabric, while it is lower for tight fabrics. For tight fabric, more fabric layers and a lower initial pressure can reduce the difference between the static and the dynamic permeability. Analytical models are used to explain and predict both static and dynamic permeability.

Keywords

analytical prediction deformation dynamic permeability woven fabric

For a porous material, static permeability defines the ability to transmit permeating fluid at a constant pressure drop, while dynamic permeability concerns mass transport under transient pressure conditions. Dynamic permeability is one of the most important properties for many technical textiles, such as automotive airbags, wearable (landing) airbags and parachute fabrics. Usually these fabrics are subjected to high initial pressure – for example, car airbag fabric can be subjected to 200 KPa. This might result in high deformation of the fabric structure, leading to a change in the permeability.

Static permeability has been studied for almost one and a half centuries since Darcy’s law (Equation (1)) was first proposed. It gives a linear relationship between pressure gradient $\frac{\partial P}{\partial X}$ (Pa/m) and fluid velocity v (m/s) under laminar flow:

(1)

where μ (Pa·s) is fluid viscosity and K (m²) is the permeability of the porous medium. Some researchers have developed analytical models to predict the fabric static permeability. Gebart¹ derived a set of expressions for fluid flow transverse to and along a unidirectional (UD) fiber array, based on fiber radius (r) and fiber volume fraction (V_f):

(2a)

(2b)

where c, C and V_fmax are 57,

\frac{16}{9 π \sqrt{2}}

and

\frac{π}{4}

, respectively, when the fiber arrangement is quadratic and 53,

\frac{16}{9 π \sqrt{6}}

and

\frac{π}{2 \sqrt{3}}

when it is hexagonal. This model had excellent agreement with experimental results when the fiber radius was adjusted to match the prediction to the experimental data. This model was developed to predict the permeability of UD fiber reinforcement. It is not accurate for fabrics, which generally comprise crimped interwoven yarns with gaps between yarns. Xiao et al.² developed an analytical model to predict the static permeability of woven fabric based on the work of Gebart,¹ Phelan and Wise³ and Kulichenko.⁴ A simplification diagram for this model is shown in Figure 1.

Figure 1.

Parabolic equation describing boundary shape of flow channel between two yarns in fabric unit cell.

This model was based on the measured geometry of the flow channel formed between yarns and has shown a close prediction compared with experimental data:

(3)

where r′ is the radius of the narrowest yarn gap, l is the half yarn width, L is the fabric thickness and δ is a geometric parameter that determines the curvature of the flow channel. This model can be used for permeability prediction when clear gaps exist between yarns, that is, loose fabrics.

The relationship between pressure gradient and fluid velocity is non-linear when fluid inertia effects cannot be ignored. This relationship was first proposed by Forchheimer in 1901 (Skjetne and Auriault⁵) to give a high-velocity correction to Darcy’s law with a power m of velocity:

(4)

where a and b are fitting constants. Based on dimensional analyses by Green and Duwez⁶ and Cornell and Katz,⁷ the coefficients in Equation (4), with m = 2, can be separated as fluid and porous medium parameters, which is today called the Forchheimer equation:

(5)

where ρ is fluid density and β is a porous medium parameter called the non-Darcy flow coefficient. Ergun⁸ suggested K and β were both functions of the porosity of the porous medium and the diameter of pores, and hence were intrinsic properties of porous media. Innocentini et al.⁹ used the Forchheimer equation (5) to determine the permeability of ceramic foams from experiments. The results indicated accurate permeability should be based on a large range of flow velocities and pressure data. Chor and Li¹⁰ developed a permeability measurement system to quantify the inter-pore connectivity of tissue engineering scaffolds. The theoretical background of the system was based on the Forchheimer equation (with a large velocity range in laminar flow), being able to characterize a wide range of permeability values. Aulisa et al.¹¹ analyzed non-linear flows of slightly compressible fluids in porous media not adequately described by Darcy’s law (Equation (1)), showing high fluid pressure can be described by a non-linear equation with an implicit permeability tensor. Dynamic permeability is usually characterized under a high initial pressure, where non-linearity between pressure and velocity cannot be ignored. The Forchheimer equation is chosen to determine dynamic permeability in this paper.

The concept of a dynamic permeability tester has been introduced by several researchers. Partridge and Mukhipadhyay¹² reported a dynamic gas-permeability tester for airbags commercially made by Textest Instruments. The dynamic tester was a table-mounted instrument that can produce a pressure load up to 200 KPa above atmospheric pressure. The gas was released through a high-speed valve and transported through a fabric test sample. The gas pressure and velocity were recorded by transducers. The experimental data indicated that the fabric structure, porosity and yarn linear density had the greatest influence on gas velocity and fabric deformation. Narayanan¹³ carried out dynamic permeability tests on airbag fabrics using a blister-inflation apparatus. The fabric was held between two metal plates as a flat sheet. When the air permeated through the fabric, the specimen deflected to form a blister. The height of the blister and the air tank pressure were measured by transducers. The experimental data showed that an increased initial pressure would lead to an increase in permeability. A tight fabric was less sensitive to the initial pressure change than a loose fabric. Wang et al.¹⁴ developed an approach based on an air shock tube to evaluate the dynamic permeability of airbag fabrics. The shock tube experiments were conducted to simulate airbag inflation. A plane air impulse was generated and impacted on the airbag fabric. The impulse was partially reflected back to the tube while the pressure was increased at the front face, leading to airflow through the fabric. The permeability was determined by measuring the velocity of the reflected shock wave. The obtained dynamic permeability was lower than the static permeability for airbag fabrics. Bandara et al.¹⁵ designed an instrument to measure the fabric air permeability at initial pressures of up to 300 KPa. The procedure was shown to be repeatable and obtained a reliable relationship between pressure and time. All experiments in this paper were carried out using this instrument, which will be described in detail in the next section.

This paper investigates the physical differences between static and dynamic permeability of woven fabric. Deformation of the woven structure under high pressure has a significant effect on permeability. Different types of fabrics are studied to identify governing parameters for the permeability. The Forchheimer equation is used to describe the non-linear relationship between pressure drop and flow velocity. Analytical models are adapted to predict permeability more accurately by considering several physical factors, in particular the initial and final fabric structure. Conclusions are given in the final section.

Experimental techniques

Design of the dynamic tester

Figure 2 shows the basic construction of the dynamic permeability tester. The tank is supplied with filtered dry air through a filter/drier F and an electrically controlled pressure regulator R. Valve V1 is used to stop the airflow into the tank once the tank is charged to the required pressure. The tank pressure and temperature are measured by a transducer G and a thermocouple S, respectively. The tank is connected to the test area through a valve V2. A fabric specimen is held between the lower clamp C1 and the upper (movable) clamp C2. Clamp C2 is controlled by an electric linear actuator that produces a clamping force of 5 KN. The clamp provides a circular test area of 50 cm². The pressure in the tank can be charged in a range of 5–300 KPa above atmospheric pressure. The tank volume is 40 liters and the working temperature range is from −10 to 100°C.

Figure 2.

Basic construction of the dynamic permeability tester.

Experimental plan

The experiments were aimed to establish (a) the difference, if any, between static and dynamic permeability; (b) the effect of initial pressure on the fabric dynamic permeability; (c) the effect of the number of layers on the fabric permeability.

The fabric specimens are listed in Table 1. Fabric cross sections were cut using a laser beam razor blade and cross-section images were obtained using a ZEISS AxioScope A1 microscope. The images were used to measure the yarn spacing (the distance between yarn center lines) and yarn width, as well as the filament radius (r) and yarn fiber volume fraction (V_f), which is the value of the cross-sectional area of total fibers in a yarn divided by the cross-sectional area of the yarn. By using the free image analysis software Image-J, the outlines of yarn cross sections were manually picked up by the Freehand selections function, and the enclosed areas were measured automatically. The geometric parameter (δ) was also obtained by fitting the curvature of the flow channel with a parabolic equation in the Image-J, a method introduced by Xiao et al.² The fabric thickness (L) was measured using the FAST-1 (Fabric Assurance by Simple Testing) device developed by the Commonwealth Scientific and Industrial Research Organization (CSIRO). A compaction pressure of 196 Pa was applied to the fabric during the measurement based on the FAST standard.¹⁶ All the measurements were repeated three to five times and the data given represent mean values.

Table 1.

Fabric specifications before dynamic tests (±standard deviation)

Fabrics	Composition and structure	Mean r (μm)	Yarn V_f	δ	L (mm)	Yarn spacing mm		Yarn width mm
Fabrics	Composition and structure	Mean r (μm)	Yarn V_f	δ	L (mm)	Warp	Weft	Warp	Weft
M	Wire mono- filament plain	25 (±0.1)	1 (±0.00)	4.90 (±0.10)	0.10 (±0.002)	0.10 (±0.003)	0.10 (±0.001)	0.05 (±0.001)	0.05 (±0.002)
U	PET65/Cotton35 Plain	5.4 (±0.3)	0.58 (±0.01)	12.96 (±0.22)	0.32 (±0.009)	0.22 (±0.032)	0.33 (±0.011)	0.17 (±0.032)	0.19 (±0.027)
A	100%Nylon plain	10.6 (±0.2)	0.70 (±0.01)	–	0.34 (±0.003)	0.53 (±0.016)	0.45 (±0.007)	0.45 (±0.007)	0.52 (±0.009)

In Table 1, the yarns in Fabric U are all made of 65% polyethylene terephthalate (PET) and 35% cotton staple fibers. The yarns are ‘Z’ spinning style from a ring spun system with twist of 858 per meter. For Fabric U, the radius is calculated as the weighted mean value of PET and cotton fiber radii according to the blend ratio. The yarns in Fabric A are made of multi-filaments without any twist and the yarn is a mono-filament in Fabric M.

The static fabric permeability was obtained by a Shirley Air Permeability Tester. The air pressure drop can be set directly and its maximum can reach up to 300 Pa. The pressure gradient was the set value divided by the fabric thickness (shown in Table 1). The test area for the sample in this instrument is 5.07 cm² (1 inch²) and airflow rate can be in the range of 0.1–350 cm³/s; these values can give the flow velocity. Each fabric was characterized five times using separate samples. Air permeability was calculated according to Equation (1) with the fluid viscosity (Pa·s). Further details of the test procedure are given by Xiao et al.²

Operating principle and data analysis

Operating principle of the dynamic permeability tester

By applying the ideal gas law for air in the tank:

(6)

where P is the absolute pressure in the tank, V is the tank volume, which is constant (40 m³), m is the mass of air in the tank at any time, R′ is the universal gas constant divided by the air molar mass and T is the absolute temperature of the air inside the tank. As air discharges through the fabric, the mass of air in the tank, as well as the pressure, gradually reduces. T is assumed constant owing to the heat capacity of the tank and the standard laboratory environment. Differentiating Equation (6) by time t gives

(7)

By applying Equation (6) to the escaped air from the tank at normal atmospheric pressure

(8)

where V′ (m³/s) is the free volumetric flow rate of air corresponding to the mass flow rate dm/dt and P_atm is the (absolute) atmospheric pressure.

Equations (7) and (8) give

(9)

The superficial velocity of air pass of the fabric (discharge per unit area) v (m/s) is

(10)

where A is the testing area. Therefore the relationship between the velocity of gas and the pressure gradient becomes

(11)

Data analysis

Curve fitting

The pressure history P as a function of time t is described by a polynomial equation that provides an excellent fit to the experimental measurement, giving a general form

(12)

where a, b,…, m, n and Const are established using a least squares technique. Then

(13)

The pressure and the velocity can be calculated at any time according to the Equations (11)–(13). A polynomial equation with order six was found to be accurate enough and the pressure and velocity can be fitted using the Forchheimer equation (5).

Analysis of experimental data

Figure 3(a) shows the data for pressure history over time obtained directly from the experiment. The data were fitted using least squares analysis for a sixth-order polynomial, Equation (12), which gives close approximation with a correlation coefficient of 0.9999. In Figure 3(b) the data of pressure gradient versus velocity were derived using the data in Figure 3(a) and substituting into Equations (13) and (11). The pressure gradient was calculated as $\nabla P = \frac{P}{L}$ . The graph gave a non-linear relationship of pressure gradient and velocity. This was not suitable for linear regression using Darcy’s law. The Forchheimer equation (5) was used to approximate the pressure gradient versus velocity. The fabric permeability K is calculated as the coefficient of the first order in the Forchheimer equation.

Figure 3.

Results (Fabric U) of (a) pressure variation over time, (b) curve fitting for pressure gradient versus velocity by Forchheimer equation.

Results and discussion

Temperature effects

The whole process of air discharge is accompanied by temperature change as measured by a thermocouple located inside the tank. The temperature drops at the initial discharging stage due to the expansion of compressed air known as the Joule–Thomson effect. Gradually the temperature climbs back after heat exchange with the environment through the open valve V2. A temperature change of 5°C was typical, as shown in Figure 4, and this is considered negligible, since T in equation (7) is absolute temperature. This shows that the assumption of a constant temperature in Equation (9) is reasonable. A constant gas viscosity of 1.83 × 10^–5Pa·s under room temperature is used, given the minimal variation in temperature.

Figure 4.

Variation of temperature in the gas tank during gas discharge (Fabric A).

Static and dynamic permeability

Fabric permeability is sensitive to fabric structure. Three different fabrics were considered in the experiments. Their structures are shown in Figure 5. It is noticeable that Fabrics U and M have clear gaps between yarns, while Fabric A is a tight fabric with yarn overlap.

Figure 5.

Fabric structures (a) Fabric M; (b) Fabric U; (c) Fabric A.

The static permeability tests of Fabrics U and A were conducted at 100 Pa and Fabric M was tested at 10 Pa due to its open structure, while the dynamic permeability tests (Equation (5)) were all conducted with an initial pressure of 120 KPa. For the latter the average calculated air velocities (Equation (11)) were all below 10 m/s, and the Reynolds numbers calculated were all less than the critical value (2300) for turbulent flow. For instance, the highest velocity and the largest hydraulic diameter were found for Fabric U, which were 6.25 m/s and 0.074 mm, respectively. Assuming flow in a circular channel, the Reynolds number was calculated as 30 (<2300). The experimental results for static and dynamic permeability are listed in Table 2.

Table 2.

Static, dynamic and analytical prediction for permeability for different fabrics (±standard deviation)

Fabric	Measured static permeability (10^–12 m²)	Predicted static permeability (10^–12 m²)	Measured dynamic permeability (10^–12 m²)	Predicted dynamic permeability (10^–12 m²)
M	36.67 (±0.36)	37.00 (Eq. (3))	36.10 (±1.65)	37.00 (Eq. (3))
U	16.43 (±0.90)	18.47 (Eq. (3))	31.35 (±1.33)	34.35 (Eq. (3))
A	0.24 (±0.01)	0.20 (Eqs. (2) & (16))	0.12 (±0.01)	0.09 (Eqs. (2) & (16))

Fabric M is a plain woven mesh of stainless steel mono-filament. Here we assume its rigidity allows no fabric deformation under high pressures. The experimental data in Table 2 show that its dynamic permeability is almost equal to its static permeability. This indicates that permeability is a constant material parameter regardless of pressure level within the laminar flow regime, provided that no material deformation occurs. The metal mesh also validates the independent measurement from the dynamic permeability tester, as it provides data in agreement with the widely accepted Shirley static permeability tester. The analytical predictions for Fabric M were based on Equation (3), using the geometric measurements as the input parameters from Table 1. The model describes accurately the geometry of the flow channel between yarns and therefore gives an accurate prediction for this fabric.

The other two materials, that is, cotton/PET Fabric U and nylon Fabric A, are likely to deform under high air pressure. Figure 6 gives the thickness of the two fabrics under different compaction pressures. The thickness was measured by the Fast-1 device by applying three different gauge pressures: 196 Pa, 1.96 KPa and 9.81 KPa.¹⁶ The curve-fitting equation for the data was chosen as a power law. Figure 6 shows that the fabric thickness reduces when the pressure increases. There is a more dramatic change for cotton/PET Fabric U than nylon Fabric A. The structure and/or the yarn fiber volume fraction V_f are likely to vary when the fabric thickness changes under high pressure, as discussed in the following sections.

Figure 6.

Thickness of Fabric U and A under different compaction pressures.

Fabric U

Fabric U is a loose fabric, as shown in Figure 5(b). The large spacing between yarns causes the majority of air to flow through these gaps. A slight change of yarn spacing can alter the fabric permeability significantly, according to Equation (3).

The parameters required in the analytical equation (3), such as yarn spacing, yarn width and fabric thickness, can be measured directly from the fabric geometry. To measure the deformation that occurs during dynamic testing, it would be ideal to obtain these values when the fabric is under high pressure. This was not technically feasible with the apparatus used here. Therefore fabric parameters were measured under a microscope from fabric samples after the test. Fabric thickness is approximated by extrapolating the power law in Figure 6 according to the dynamic test pressure. The geometrical parameter δ is assumed from a simple relationship with thickness:²

(14)

where L is fabric thickness and l is half of the yarn width.

The microscopic images in Figure 7 show a visual change in yarn spacing and width for Fabric U after the dynamic permeability test. Measurements from the images provide a set of comparative values, as listed in Table 3, including the calculated thickness and geometric factor.

Figure 7.

Fabric U (a) before dynamic test; (b) after dynamic test.

Table 3.

Geometry change of Fabric U

Fabric U	Yarn spacing mm		Yarn width mm		Fabric thickness L (10^–4 m)	Flow channel shape factor δ
Fabric U	Warp	Weft	Warp	Weft	Fabric thickness L (10^–4 m)	Flow channel shape factor δ
Static	0.223	0.331	0.174	0.192	3.19	12.96
Dynamic	0.220	0.353	0.166	0.198	1.42	7.50

Based on the values in Table 3, predicted values for both static and dynamic permeability (Equation (3)) were calculated as listed with the experimental results (Table 2). Both predictions are close to the experimental permeability values. Equation (3) is useful for dynamic permeability prediction, provided that fabric deformation is measured soon after the dynamic permeability test. The analytical model offers insight to explain the difference between dynamic and static permeability. Under high pressure the gap between yarns increases, while the fabric thickness and the flow channel shape factor δ decrease. These changes explain why the fabric permeability is higher for the dynamic permeability test.

Fabric A

Fabric A is a tight airbag fabric with overlapping yarns with no clear spacing, as seen in Figure 5(c). Compared with the thickness reduction of 42% for Fabric U, as shown in Figure 6, Fabric A has a thickness change of only 10% from compaction pressure 196 Pa to 9.81 KPa. This is due to the tight structure and high yarn V_f for this fabric. The space between fibers in yarns is the main flow channel for tight fabrics. The Gebart model (Equation (2)) for fiber bundles is suitable for tight fabric permeability prediction. For this fabric, the dynamic permeability decreases by half compared with the static permeability, as shown in Table 2. This trend is opposite to the loose Fabric U, which shows a higher dynamic permeability. A similar experimental observation was found in the work of Wang,¹⁴ where fabrics became less permeable under a high-pressure air impulse.

In the dynamic permeability test, the fabric was deflected and stretched by high pressure. As dynamic permeability is lower than static permeability, this indicates that gaps did not open between yarns in the dynamic test and the fabric became much tighter. The yarn fiber volume fraction V_f becomes larger under high pressure when the fabric thickness reduces and fiber bundles are compacted together tightly. According to the hexagonal packing theory, the maximum achievable fiber volume fraction (V_f) is 0.907. The corresponding pressure is 1.8 × 10¹⁰Pa, which is the upper bound of pressure for the fitting equation (15). Assuming no other geometric deformation, yarn thickness reduction alone offers an increased fiber volume fraction $V_{f}^{'}$ :²

(15)

where V_f is the measured original yarn fiber volume fraction from microscopic analysis of the un-deformed yarn cross section, L is the original fabric thickness and L′ is the thickness under a high pressure extrapolated from the power law in Figure 6. This suggests a yarn V_f increase from 0.70 to 0.75. Based on this method, Equation 2(a) would suggest static and dynamic permeabilities of 1.86 × 10^–13 m² and 0.82 × 10⁻¹³ m², assuming flow transverse to the yarns only.

However, Gebart’s model (Equation (2)) gives an under-estimated prediction compared with experimental results. This model was originally developed for UD reinforcement. The model needs to be adapted here to account for the woven fabric structure, such as fiber orientation due to yarn crimp and non-uniform fabric thickness due to elliptical yarn cross section. Figure 8 shows the two features that should be considered for applying the Gebart model to woven fabric. Firstly, the through-thickness flow path has an angle α to the fiber axis, as shown in Figure 8, where α is the smallest value measured along the crimped yarn. Advani et al.¹⁷ proposed an equation that can correct the fabric permeability based on the transverse permeability (K_⊥) and parallel (K_‖) to the fiber bundles:

(16)

Figure 8.

Fabric A indicating yarn crimp and non-uniform fabric thickness.

Here the angle α was measured at 69.5° from an un-tested sample (representative of the geometry for static testing) and 74.5° from a sample after dynamic testing. The predictions in Table 2 show that Equation (16) increases the permeability by 10%, bringing it closer to the experimental values.

Secondly, the fabric thickness varies across the sample, as is clear in Figure 8. Hence there is non-uniform airflow through the fabric, and in particular the areas between adjacent yarns with maximum crimp are likely to exhibit lower resistance to flow than the yarn crossovers. This may explain why the predictions in Table 2 are still around 20% lower than experimental values. This effect is difficult to describe using a purely analytical approach, and it is likely that this can only be captured using a technique such as computational fluid dynamics.

Effect of initial pressure on the fabric permeability

Figure 9 compares the pressure history for different initial pressure levels in the dynamic test. The curve-fitted polynomial equations provide a good fit over the region of interest for all tests. Figure 9 also shows that higher initial pressure leads to a longer period of discharge.

Figure 9.

Air discharge pressure history with different initial pressures for Fabric A.

Figure 10 gives three different initial permeability values along the pressure history. The raw data of pressure versus time are firstly filtered using Equations (12) and (13) to remove the effects of electrical noise caused by the pressure transducer during the experiment. The initial permeability corresponds to pressure at an early discharge stage. As it is a small section of the entire pressure range, the initial pressure and flow rate are assumed to follow Darcy’s law (Equation (1)). From Figure 10, a decrease in initial pressure leads to an increased permeability, with the data tending towards the static permeability value (2.4 × 10^–13 m²) at low pressure.

Figure 10.

Initial permeabilities with different initial pressures for Fabric A.

Effect of multiple fabric layers on the permeability

Table 4 gives experimental results for static and dynamic permeability of Fabric A with different numbers of layers. Each experiment was repeated five times. The standard deviation of measurement is less than 5%. The experimental data show that an increase in the number of fabric layers leads to a small increase in static permeability. The dynamic permeability is in general smaller than the corresponding static value. The reason has been discussed in the Static and dynamic permeability section. By increasing the number of fabric layers, the difference between the static and dynamic permeability is decreased, as the dynamic permeability increases with more layers. The reason might be a relatively smaller deformation for more fabric layers under the same initial pressure, as is shown in Figure 11.

Figure 11.

Schematic comparison of fabric deformation under the same pressure for different numbers of layers.

Table 4.

Static permeability (100 Pa) and dynamic permeability (120 KPa) of Fabric A with different numbers of layers

Number of layers	Static permeability (10⁻¹² m²)	Dynamic permeability (10⁻¹² m²)
1	0.24 (±0.01)	0.12 (±0.02)
2	0.25 (±0.01)	0.20 (±0.01)
3	0.27 (±0.01)	0.23 (±0.01)

Figure 11 compares deformation for different numbers of fabric layers under the same uniform pressure load. According to Timoshenko and Woinowsky’s¹⁸ large deflection plate and shell theory, Equation (17) is derived based on a Poisson’s ratio of 0.3 for qualitative comparison. The Poisson’s ratios for most fabrics are in the range of 0.2–0.5.^19,20 This shows that the maximum displacement (w_max) at the center of the solid thin plate is related to its thickness (L):

(17)

where P is the uniform pressure on the sample, R is the sample radius and E is the Young’s modulus. Here fabric is assumed to behave as a solid thin plate for simplicity. Thinner fabric samples will hence lead to larger deflection, based on Equation (17). For airbag Fabric A, a single layer with the largest deflection causes yarn de-crimping and tensioning without introducing inter-yarn gaps. The contact force at yarn crossovers increases as a result, which acts to compress the yarns leading to an increase in yarn V_f, resulting in a reduced fabric permeability, based on Equation (2).

Conclusions

Dynamic permeability is obtained by discharging air with high initial pressure through woven fabrics. The transient pressure causes fabric structural deformation. The behavior is different from the static permeability test, applying a constant small pressure drop. The Forchheimer equation, describing a non-linear relationship between pressure and velocity, is used to analyze the dynamic experimental data. The experimental data for the metal mesh fabric show no difference between static and dynamic permeability, because the fabric structure was not changed under high pressure. This also validates the dynamic permeability test method compared with the widely accepted Shirley static permeability test. Most fabrics are less rigid and are prone to deformation during the dynamic permeability test. One example is a cotton/PET fabric with a loose structure, which is easily deformed under pressure. The dynamic permeability for this fabric is much higher than its static permeability. An analytical model shows that the increase in yarn spacing due to fabric deflection leads to higher permeability. In contrast, a tight fabric, such as the nylon airbag fabric, had a lower dynamic permeability than its static value. High pressure applied to this fabric results in a higher yarn fiber volume fraction, leading to a lower fabric permeability. Experiments also show that more fabric layers would have a larger dynamic permeability for tight fabric. It is proposed that this is due to reduced deflection, which in turn causes less compaction at yarn crossovers and hence higher yarn permeability. The next stage in this work will attempt to predict the deformation that occurs during dynamic testing and to combine this with the analytical modeling approach used here to provide a fully predictive through-thickness permeability model.

Footnotes

Acknowledgements

The authors would like to thank United Wire Ltd and Airbags International Ltd for providing experimental materials, and Leeds University for undertaking the experimental tests.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Conflict of interest statement

None declared.

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