Carbon-fiber reinforcements for epoxy composites with electromagnetic radiation protection—prediction of electromagnetic shielding ability

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Abstract

The development of flexible air/water vapor permeable composites designed for shielding the electromagnetic field has received an increasing amount of attention in recent years. A great deal of the attendant research has dealt with the development and investigation of electromagnetic shielding (SE) composites with textile-based reinforcements. However, little attention has been paid to the simple prediction of their SE ability, especially in terms of industrial applications. In this study, we investigated the design and properties of carbon-fiber reinforcements for use in epoxy composites that provide SE protection. Here, we selected the Aksaca electrically conductive continuous carbon-fiber roving and prepared different reinforcements with woven structures before investigating the effects of the weft and warp sett and the thickness of the warp and weft threads on the SE ability. To measure the shielding effectiveness, we used the coaxial transmission line method, while an analytical approach was adopted to predict the shielding effectiveness of the carbon reinforcements and to compare the calculated values with the experimental data. The SE effectiveness of the reinforcements varied from 10 to 45 dB at a frequency of 1.5 GHz, with good agreement between the calculated and experimental results.

Introduction

Electromagnetic interference can be defined as the electromagnetic radiation produced by electrical circuits that can adversely affect the operation of surrounding electronic devices or cause damage to living organisms. In recent decades, the level of so-called electromagnetic smog has increased significantly, especially that related to the development of new high-frequency electronic systems and telecommunication equipment. This phenomenon has led to the active development of new and effective solutions for the provision of shielding from interfering electromagnetic radiation in various applications.

Electromagnetic interference shielding refers to the blocking of incoming electromagnetic waves through absorption, reflection, or multiple reflection, whereby the shielding material resists penetration by the electromagnetic radiation.

The attendant literature reveals that the most common method used for the shielding from electromagnetic fields involves reflection via metallic materials, generally foils or plates. The disadvantages of these solutions include their limited flexibility due to the high rigidity and high density of these materials, as well as certain corrosion issues and the limited capacity to control the efficiency of the electromagnetic shielding (SE). In addition, electromagnetic smog cannot be eliminated via reflection from a shield alone. Therefore, an increasing amount of attention is being paid to the development of absorbent polymeric-based shielding materials, which have the advantages of having a low weight (density of >2 g/cm3 compared with metals with densities of >3 g/cm3) and being comparatively inexpensive and formable. However, most polymeric materials are electrical insulators that are entirely transparent to electromagnetic radiation. By incorporating an electrically conductive component of any one of various types and shapes, shielding from the electromagnetic field can also be achieved. As such, composite materials are gaining popularity [[1], [2], [3]]. Carbon-fiber (CF)-reinforced polymers are a special type of composite material in which the CF provides strength, stiffness, and electrical conductivity, while the polymer provides a cohesive matrix that protects and holds the fibers together. This type of composite material is most commonly used in the aircraft industry.

In fact, CF is electrically conductive due to the planar layered structure of the carbon atoms, which provides a certain degree of SE for materials containing CFs in their structure. As such, CFs are preferred to other forms of carbon filler, such as graphite or carbon black [4]. However, since the cost of CFs is almost four times higher than that of traditional polymer materials, the CF content becomes critical in this type of composite. Various researchers (e.g. Refs. [[5], [6], [7], [8], [9]]) have demonstrated that the SE can be improved and that the amount of CF used can be reduced by controlling the discontinuous CF orientation. In Ref. [7], it was demonstrated that the higher the CF content, the higher the SE, with the orientation of the CF perpendicular to the casting of the composite film providing even higher SE (up to 150 dB/mm at f = 10 GHz). It has also been confirmed that a high aspect ratio (ratio of the length of a fiber to its diameter) is preferable [10]. Meanwhile, the experiments performed in Ref. [11] indicated that both the electric conductivity and the SE of a given composite will increase with a higher short CF content (a composite with a filler loading of 30 phr has an SE of approximately 60 dB at a frequency of 10 GHz), while the dependence of the SE on the electric conductivity can be approximated using a logarithmic function. The SE value also tends to increase with an increase in composite thickness, while the magnetic permeability of any given composite will increase with a higher short CF content and with an increase in frequency.

Compared with the traditional discontinuous CFs, a composite with higher SE can be realized through the use of continuous CFs as a woven reinforcement under the same conditions (e.g., the CF content) [12]. The mechanism behind this improvement is the formation of a highly electrically conductive symmetrical network of carbon multifils (containing thousands of closely arranged fibers), which are required for SE. Another reason for the higher SE of this type of composite relates to how reflection is a dominant factor in the total shielding effectiveness [13]. The preparation and properties of continuous CF-reinforced composites have been reported in a number of studies [[14], [15], [16], [17]]. For example, nickel-coated CF-reinforced composites were studied in terms of their mechanical properties and their ability to shield the electromagnetic field in Ref. [17]. Here, in addition to achieving unique mechanical properties, it was found that the SE increased from 20 to 30 dB due to metallization. In Ref. [16], the authors demonstrated how the SE of their carbon fabric/epoxy samples increased with a higher fiber volume fraction (the resin reduced the contact between the fibers). Despite the fact that a larger thickness and a greater number of fabric layers of the composite does not provide higher electric conductivity, specimens with more layers tend to demonstrate greater protection against electromagnetic radiation. It can thus be stated that the SE is not only related to the conductivity of the material but is also dependent on the power that is dissipated along the thickness and reflected at different interfaces.

The SE is the key parameter in the evaluation of the electromagnetic compatibility of electronic systems. One of the most important factors in reducing the SE relates to the presence of apertures on the surface of the shielding enclosure [18]. However, in practical applications, apertures are both desirable and necessary for ensuring sufficient air permeability, ventilation, and cooling, as well as ease of maintenance. In this context, less attention is generally paid to the structure of the carbon fabric reinforcements, especially in terms of weave and related porosity. A woven reinforcement in a plain weave of continuous carbon, boron, and carbon–boron fibers was studied in Ref. [19]. Here, the authors found that the highest SE (around 45 dB for a frequency of 1.5 GHz) was provided by the CF due to its higher electrical conductivity compared with boron fibers. However, more details regarding the structure of the woven reinforcements (e.g., the sett of the warp or weft, the fineness of the multifils or fibers) were not reported. Meanwhile, the SEs of plain weave, balanced twill weave, and uniform-direction conductive continuous CFs were studied in Ref. [12], with the experimental results indicating that the SEs of the composites containing woven reinforcement were higher than those obtained with the uniform-direction CF at the same weight percentage content. In fact, the highest SE of 96 dB was obtained with two balanced twill-weave reinforced composites. Elsewhere, a number of hybrid and 100% carbon woven fabrics were investigated in Ref. [20], with the authors comparing various different patterns, including plain, twill, and satin weaves. Here, as was expected, the plain and twill weaves, which were made of 100% continuous CF roving, achieved a higher SE than the satin, which was attributed to the number of intersection points. Meanwhile, in Ref. [21], various designs of frequency-selective composites containing reinforcements woven from continuous CFs and dielectric fibers in periodic patterns were outlined.

Overall, the literature review revealed that to obtain a fabric with a high capacity to shield against the electromagnetic field, it is advantageous to use continuous, highly electrically conductive CFs, with the plain-weave-type being the preference.

Recently, an increasing amount of attention has been paid to the effective evaluation of the SE using non-experimental methods, which can be divided into two main categories. The first involves full-wave solvers based on numerical methods, such as the finite-difference time domain, the method of moments, the transmission line matrix, and various hybrid methods [18,22,23]. The disadvantage of these methods lies in the complexity of the associated computing resources and computer memory. The second non-experimental category involves analytical methods used for the rapid computation of the SE for certain structures in widespread use, such as rectangular enclosures.

With respect to textile-structure-based shielding materials, a limited number of scientific papers have dealt with the attendant SE simulation or prediction. For example, in Ref. [24], the authors formed a three-ply continuous CF woven (satin weave) reinforced composite and simulated the SE using the plane-wave shielding theory. However, the simulated SE results were not in good agreement with the experimentally measured SE. In Ref. [21], the electromagnetic characteristics of a frequency-selective fabric composite (plain weave of continuous CF with square elements with an 8-mm aperture) were simulated using CST Microwave Studio 5.1 software and the data related to the electrical conductivity, fiber undulation, and aperture-to-cell ratio of carbon rovings, with the results being in excellent agreement with the experimentally measured data. In Ref. [16], the CST Microwave Studio software was also used for SE simulation, with the results again demonstrating good agreement with the experimental results, especially with the thin compact carbon woven/epoxy samples. The SE of hybrid fabrics containing different contents of staple stainless-steel fibers was predicted in Ref. [25] based on the assumption that the total SE of a fabric is a linear combination of the SE due to apertures (SEaper) at high frequencies and the SE of compact materials at low frequencies (SEsheet). Here, all equations were taken from the published literature, with good agreement obtained only for samples with lower electric conductivity and apertures of smaller dimensions. Reference [26] includes a detailed derivation of SE for SEfabric and SEaper, with a general equation of SE derived for woven fabrics made of blended yarns with high conductivity (σ > 244 S/m), which was then compared with the experimental data with absolute agreement. However, the derived calculations were somewhat complicated.

All the above research indicates the need for both deeper research into the SE efficiency of carbon-based woven fabrics in terms of their structure, especially the porosity, and the verification of the possibility of SE prediction based on the knowledge of the geometric parameters and electrical conductivity of rovings. With this in mind, the current research was aimed at experimentally identifying the factors that affect the SE ability of CF woven reinforcements, while a further crucial objective was to verify an uncomplicated approach suitable for calculating the SE of woven, electrically conductive reinforcements based on various input parameters. As such, we used the coaxial transmission line method, the ASTM 4935-18 standard method, to experimentally investigate the SE of composite reinforcements with woven structures made of carbon continuous multifils. This standard is one of the most commonly used standards for the SE evaluation of planar materials. We also selected this standard in view of the intended use of the composite, that is, within the aircraft industry. Avionic systems contain numerous onboard, frequency-generating systems, including frequency synthesizers, digital circuits, telemetry systems, and switching power supplies. Therefore, SE in the frequency range starts at VHF radio frequencies, while ending at L-band microwave frequencies is desirable. Specifically, we explored the effects of the warp and weft sett and multifil fineness on the SE. Given that the geometry of a bonded-junction wire-mesh screen is highly similar to that of low-density woven fabrics made of electrically conductive threads, we were able to use an extremely simple analytical computation method [27] to predict the SE based on the knowledge of only a small number of parameters, i.e., the geometrical properties of the woven fabric (length of aperture and diameter of multifil) and the electrical conductivity of the carbon multifil. Following this, we compared the SE values obtained experimentally with those computed analytically, with the findings subsequently discussed.

The SE ability of any shield varies depending on the frequency, geometry, and material of the shield, as well as the type of attenuated field, the angle of incidence, and the polarization [26]. The total SE of a solid material with no apertures (SEsheet) is equal to the sum of the absorption loss (A), the reflection loss (R), and a correction factor to account for multiple reflections (B) in the shield. In contrast, the term B can be neglected for electric fields and plane weaves [26]:SEsheet=10log101|S21|2=Asheet+Rsheet+Bsheet=10log1011|S11|2+10log101|S11|2|S21|2=20log10EiEt=20 log10HiHt=10log10PiPt,where Ei, Hi, and Pi are the electric field intensity, magnetic field intensity, and power, respectively, measured without the presence of the tested material, while Et, Ht, and Pt are the same physical quantities measured in the presence of the tested material, and Sij represents the scattering parameters [28].

The absorption loss and reflection loss of the shield with no apertures can be written after simplification as follows [29]:Asheet=0.0848tKKCf,Rsheet=C+10log(KKCf),where C is the constant, K [S·cm−1] is the volume conductivity, KC is the copper conductivity, f [MHz] is the frequency, and t [m] is the thickness of the shield.

In the previous formulations, a solid shield with no apertures was assumed. In practice, however, most shields are not solid. In the case of fabrics, the inter-yarn pores represent the apertures. All types of discontinuities (e.g., seams, ventilation holes, etc.) considerably reduce the effectiveness of the shield, while with a higher frequency, the intrinsic SE of the shield material is of less concern than the leakage through the apertures [30,31]. The total SE of a porous material can be expressed as a linear combination of the SE due to apertures at high frequencies and the SE of compact materials at low frequencies [31]:SE=e0.017LfSEsheet+(1e0.017Lf)SEaper,where L is the maximum aperture length and SEaper is the SE of an aperture depending mainly on the geometrical dimensions of the aperture. More details regarding different approaches for the calculation of SEaper can be found in Refs. [31,32].

Woven structures, especially in the plane wave, have a similar geometry to wire mesh, meaning a simple analytical solution for the SE can be applied. Assuming that the aperture dimensions are small relative to the wavelength, the SE of a planar mesh screen with bonded junctions can be described using the equivalent sheet impedance of the mesh [33]. The power transmission coefficient or the total shielding effectiveness (in dB) can be calculated based on the electrical conductivity and radius of the wire, the length of the aperture (see Fig. 1), and the angle of the incidence as follows:SEtot(ω,θ)=10log10{|T1(ω,θ)|2+|T2(ω,θ)|2},where ω is the angular frequency (ω=2πf), f [Hz] is the frequency, and T1(ω,θ) and T2(ω,θ) are the transmission coefficients for the polarization of the transverse electric and transverse magnetic modes, respectively, which can be calculated using the following equations:T1(ω,θ)=(2ZS1(ω)Z0)cosθ1+(2ZS1(ω)Z0)cosθ,T2(ω,θ)=(2ZS2(ω)Z0)cosθ+(2ZS2(ω)Z0),where Z0 is the free-space impedance (Z0 = 376.730 Ω), and ZS1 and ZS2 are the eigenvalues of the mesh impedance operator, which are given as follows:ZS1(ω)=Zωa+jωL,ZS2(ω)=ZS1jωL2sin2θ,where a [m] is the length of a square aperture, Zω is the wire impedance per unit length (approximated by its DC electrical resistance per unit length), and L is the sheet inductance. These variables can be calculated as follows:L=μ0a2πln{(1e2πr/a)1},Zω=(πr2σ)1,where μ0 is the vacuum permeability (μ0=1.256·106 H/m), r [m] is the wire radius, and σ [S/m] is the electrical conductivity.

The relationships described above are primarily intended for meshes with square apertures; however, it was reported in Ref. [27] that non-square (hexagonal) aperture meshes can also be handled with an aperture of an equivalent square-area shape.

Section snippets

Electrical characteristics of fibers and threads

The resistance, R, of a wire of fiber (annular cross section) with length L can be calculated using the following formula:R=LρA=4Lρπd2,where R [Ω] is the resistance of the conductor, L [m] is the length of the conductor, ρ [Ω·m] is the electrical resistivity of the conductor, A [m2] is the cross-sectional area, and d [m] is the nominal diameter of the fiber [34].

Meanwhile, the electric resistivity, ρ, also known as specific electrical resistance [Ω·m], is a measure of how strongly a wire

Continuous carbon-fiber roving

To prepare the woven reinforcements, we used Aksaca carbon roving, type A-35, which is comprised of continuous fibers of a polyacrylonitrile precursor, the main physical and chemical properties of which are shown in Table 1. Meanwhile, Fig. 2 presents microscopic images of the CFs in carbon roving A-35.

Carbon-fiber woven reinforcements

Using the carbon roving, we created eleven types of reinforcement in the form of a plain weave fabric with a different total warp and weft sett. The same method was used to prepare all the

Electrical properties of the carbon roving

Fig. 7 shows the dependence on the clamping length L of the electrical resistance R and of the electrical resistance when considering the fineness of the carbon roving R·T·10−5. Here, the linear least squares method was used to fit the model to the data. The slope of the linear regression model indicates the RL and RS values in accordance with Equations (15), (17)), while the intercept of the regression line represents the sum of the contact resistances at the interface between the material and

Conclusion

In this paper, we investigated the CF reinforcements used in the preparation of SE epoxy composites. A total of seven plain-weave samples were created using carbon roving (fineness of single carbon roving T = 196 tex) for the weft and warp threads. The samples differed in the two following respects: warp and weft sett (spacing between threads) and warp and weft thread thickness (by combining two and three carbon rovings).

First, we experimentally determined the SE efficiency according to the

Author statement

Veronika Tunakova - conceptualization, methodology, experimental, original draft preparation.

Maros Tunak - data curation, visualization, software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was a supported research project CZ.01.1.02/0.0/0.0/15_019/0004465 entitled Extreme shielding textile materials for special applications granted by the Ministry of Industry and Trade of the Czech Republic and the Ministry of Education, Youth and Sports of the Czech Republic and the European Union – European Structural and Investment Funds in the frames of Operational Programme Research, Development and Education – project Hybrid Materials for Hierarchical Structures (HyHi, Reg. No.

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