Robust Electrical Contact With Low Interface Resistance Using Embedded Co-cured Electrodes in Carbon Fibre Composites

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Wadge, J. D. Acosta, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5639196/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Jun, 2025 Read the published version in Applied Composite Materials → Version 1 posted 11 You are reading this latest preprint version Abstract Achieving robust low-resistance electrical contact with carbon fibres embedded in polymeric matrices is a challenge and different electrode fabrication methods, mostly for after composites are cured have been examined in the literature. This paper investigates the use of metallic foils co-cured on the top surface of carbon fibre reinforced polymer (CFRP) composites to form stable electrodes. Different electrode materials and the effects of their geometry variation on the CFRP to electrode interface resistance (IR) are studied experimentally. Finite element (FE) analysis is used to estimate the spread resistance (SR), providing a reliable estimation of the interface resistance between different electrodes and CFRP specimens. Copper is found to be the optimal electrode material and has a low interface resistance per unit electrode area ranging from 2.75×10 − 4 Ωmm − 2 to 1×10 − 3 Ωmm − 2 independent of geometry parameters. The mechanical bonding between the electrodes and the composite has been examined using pull-off tests and the obtained results show that the electrodes have an acceptable mechanical bonding with the composite layer. In comparison to other electrode fabrication processes, the co-curing technique is significantly easier, less invasive and more cost-effective as it eliminates the need for altering or introducing surface damage to CFRP specimens. Contact Resistance Electrical properties Longitudinal Resistance Co-Cured Electrodes Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 1 Introduction For decades, researchers have studied the self-sensing functionalities of carbon fibre composites for various structural health monitoring approaches. Such studies have typically included monitoring the health of a structure in real time using resistance measurements to develop damage detection and early warning capabilities [ 1 ], [ 2 ]. Any change in resistance of carbon fibre reinforced polymer (CFRP) laminates has been reported to indicate the development of internal damages, e.g. fibre breakages or delamination. Furthermore, studies have evaluated CFRP in various loading conditions and the feasibility of using the electric resistance change method to assess the structural integrity of composite materials while in service [ 3 ]–[ 7 ]. These methods highlight the need to accurately capture CFRP resistance measurements directly linked to the physical changes within the material to infer practical sensory applications. Typically, it is difficult to establish good electrical contact between carbon fibres in composites and external sources of electrical power as fibres are embedded in a polymer matrix. This can result in high 'apparent electrical resistance' being observed. This apparent high contact resistance is caused by the matrix acting as a barrier impeding a good electrical continuity. This issue can be addressed using a conductive intermediary material known as electrode, which is applied to bridge the connection between carbon fibres and the external source of electrical power. The primary function of an electrode is to provide a uniform and stable connection with an external electrical source, e.g. measuring probes to determine the resistance of the system. Figure 1 summarises different electrode fabrication techniques grouped into two main categories: (i) electrodes co-cured along with the CFRP composite and (ii) electrodes manufactured on cured composite following surface preparation. Several studies have experimented introducing electrodes on cured CFRP specimens using various complex and expensive fabrication techniques. These include methods like conductive metal foil with applied external pressure [ 8 ]–[ 14 ], conductive paints [ 5 ], [ 15 ], electrolytic deposition or electroplating [ 2 ], [ 13 ], [ 16 ]–[ 18 ] sputtering [ 19 ]–[ 22 ], sintering [ 23 ]–[ 25 ] and soldering [ 2 ], [ 26 ] as depicted in Fig. 1 . All of these methods require different forms of extensive surface preparation as a first stage to remove the insulating matrix layer, before applying the electrode material to the carbon layer, which is time consuming, need specialist facilities and is labour intensive. The most common surface preparation step employed is surface sanding, grinding or the use of a laser [ 27 ]. In addition to mechanical polishing, sample surface edges undergoing chemical polishing have also been reported [ 13 ]. Sanding usually involves rigorous manual abrasion carried out using sandpaper (SiC-paper grit 320 to 1000) followed by polishing and the specimen is cleaned afterwards with acetone to remove debris particles. Sanding the CFRP surface can often lead to non-repeatable results, damage to carbon fibres and variability in different specimens. After sanding and polishing the surface Laudani et al. used copper tapes and secured it using conductive silver paint [ 14 ]. In addition, they applied 20 MPa pressure on the metal electrodes through a hydraulic press to mitigate the effects of surface roughness and improve the ohmic contact. Many studies have used copper strips or foils mechanically held by plastic grips [ 8 ], screw actuator [ 9 ], magnetic nails [ 10 ], bench vice [ 11 ], [ 12 ] or springs [ 13 ] to apply pressure on the electrodes to improve the contact between the electrodes and CFRP to aid reproducibility of the measured electrical resistance. These special arrangements to promote direct electrode contact with carbon fibre are not straightforward and is not practical in real use case scenarios. Contact resistance (CR) between electrodes and CFRP laminates comprises two key elements: interface resistance (IR) and spread resistance (SR). Interface resistance determines the electrical current flow across the boundary between the electrodes and the CFRP laminate. Factors such as surface roughness, oxide layers, imperfect contact, material property mismatch and surface contamination contribute to interface resistance. Whereas, spread resistance arises due to the finite size of the contact area between metallic foils and CFRP composites. It reflects how easily current can spread through the CFRP laminate. The arrangement and configuration of electrodes significantly impacts spread resistance, however these aspects do not affect the resistance at the interface between the electrode and CFRP laminate. For instance, edge electrodes applied to the full edges of a CFRP laminate exhibit minimal spread resistance because the current is already evenly distributed through the thickness. However, a surface electrode is only in contact with surface carbon fibres, and therefore experiences non-negligible spread resistance. In this case, the current introduced at the sample’s surface must navigate a restricted area before evenly spreading through the CFRP laminate’s thickness. In the literature, the interface resistance, \(\:{R}_{interface}\) and spread resistance, \(\:{R}_{spread}\) , are not separately discussed and only the contact resistance, \(\:{R}_{contact}\) , in electrodes applied post curing of the CFRP have been reported using different techniques [ 14 ], [ 16 ], [ 28 ], [ 29 ] depicted in Fig. 1 . This information is not quantitatively reported for co-cured electrodes. Co-curing rectangular copper foil electrodes [ 3 ], using flexible printed circuit boards [ 7 ] and embedding conductive wires [ 30 ], [ 31 ] during the composite lay-up stage of a CFRP specimen to achieve electrical connection have been used in cases for damage detection. To the authors’ best knowledge, no paper has individually studied the co-curing technique in itself detailing its ability to achieve a stable, reproducible, and low contact resistance electrical connection in CFRP composites. With electrodes being applied to the top surface of prepregs before curing the composite, the need for surface preparation and the risk of surface damage is eliminated. Different parameters such as electrodes thickness, length, width offset, material, and the CFRP fibre areal weight are examined in this paper to understand their effects on the contact resistance and more specifically on interface resistance. Finite element (FE) method is used to estimate spread resistance in different CFRP layers with varying thickness. This allows to calculate the interface resistance between the electrodes and CFRP laminates from the experimental contact resistance results. These aspects have not been studied previously and are important in informing the optimal electrode geometry parameters. This paper integrates FE analysis and experimental validation to quantify the effects of electrode geometry, material, and alignment on both electrical and mechanical performance. 2 Concept Electrode materials are applied on the uncured CFRP prepregs and then co-cured together under pressure and heat as shown schematically in Fig. 2 . The matrix is not solidified at early stages of the curing cycle and the external pressure applied in autoclave can press the electrodes into the CFRP. This increases the possibility of achieving a good contact between the carbon fibres and the electrode before the matrix is set. After completion of the curing cycle, the electrodes are embedded in the carbon fibre layer with a flush top surface. Attaching probes on these electrodes will establish the electrical connection needed for monitoring systems. In this paper, two co-cured electrode concepts are tested: (i) electrically conductive metal foil and (ii) thermosetting conductive paint. This technique does not require any surface post processing after the composite is cured. It is significantly easier, robust and lower cost compared to those fabrication processes that apply electrodes to the composite after curing. The post-cure methods often involve energy-intensive processes and can lead to material wastage due to surface preparation steps. In contrast, the co-curing technique simplifies electrode integration, reducing energy consumption and minimising material waste, thereby offering a more sustainable alternative for large-scale manufacturing. This makes it particularly suitable for high-performance applications such as aerospace, automotive, and energy systems, where both reliability and cost-efficiency are critical. 3 Contact resistance and CFRP resistance The longitudinal electrical resistivity of CFRP composites along the fibre direction is significantly lower than the transverse resistivity and through-thickness resistivity [ 1 ], [ 5 ]. This paper is focused on the longitudinal resistance of unidirectional (UD) CFRPs and the effects of electrodes on the measured resistance. The experimentally measured total resistance, \(\:{R}_{Total}\) of the composite has a non-zero contact resistance, \(\:{R}_{contact}\) at each of the two measuring electrodes that is added to the theoretical CFRP resistance \(\:{R}_{CFRP}\) as shown in Eq. ( 1 ). This equation assumes a uniform current distribution in the thickness direction, providing a simplified framework for calculating longitudinal resistance and is validated using FE simulations as explained later. $$\:{R}_{Total}={R}_{CFRP}+\:2\times\:{R}_{contact}$$ 1 The contact resistance, \(\:{R}_{contact}\) , has two elements as shown in (2). $$\:{R}_{contact}=\:{R}_{interface}+{R}_{spread}$$ 2 Interface resistance, \(\:{R}_{interface}\) , is the electrical resistance that arises at the interface between the electrode and the adjacent carbon fibres. The second factor is the spread resistance, \(\:{R}_{spread}\) , which arises when current flows from a small contact area into a larger region of the bulk material. As the current spreads out from the confined contact area into the larger bulk, it encounters resistance due to the constrained flow paths and current crowding effects [ 32 ], [ 33 ]. In an ideal case if the electrodes contact have zero interface resistance, and if the electrical current is uniformly spread between the two electrodes having zero spread resistance, the measured total resistance of the composite would be equal to the CFRP resistance, \(\:{R}_{Total}\:\) = \(\:{R}_{CFRP}\) . With a low contact resistance, \(\:{R}_{Total}\) and \(\:{R}_{CFRP}\) would be close but not exactly equal. CFRP resistance, \(\:{R}_{CFRP}\) , is the resistance between the electrodes if the current is uniform. Using Ohm's law of electrical resistance, the CFRP resistance can be written as Eq. ( 3 ) to estimate the longitudinal fibre direction resistance of the composite. $$\:{R}_{CFRP}=\:{\lambda\:}_{el-0}\:\frac{d}{{A}_{c}}={\lambda\:}_{el-f}\:\frac{d}{{A}_{f}}$$ 3 Where \(\:{\lambda\:}_{el-0}\) is the fibre-direction CFRP electrical resistivity, \(\:d\) is the shortest distance between the inner edges of the two electrodes as shown in Fig. 3 and \(\:{A}_{c}\) is the total cross-sectional area of the CFRP between the two electrodes. Only the carbon fibres are the conductive medium and the polymer matrix has a significantly higher resistivity. Therefore, it is possible to estimate the CFRP resistance based on the resistivity of the carbon fibres, \(\:{\lambda\:}_{el-f}\) and the total area of all the carbon fibres between the two electrodes, \(\:{A}_{f}\) , as shown in the right-hand side of Eq. ( 3 ). The electrodes used in this research have a thin rectangular flat shape with resistance values significantly lower than that of composite. Hence, in Eq. ( 3 ) it is assumed that the apparent resistance between two electrodes in the fibre direction \(\:{R}_{CFRP}\) , is independent of where the probes of the ohm meter touch the electrodes. This has been confirmed using the FE analysis as will be explained later. The analytical equations for \(\:{R}_{CFRP}\) provide the lowest possible electrical resistance between two surface electrodes as it assumes a uniform current between the electrodes. Non-uniform electrical current due to current spreading in the thickness direction increases the total electrical resistance between the electrodes and is accounted for in the spread resistance, \(\:{R}_{spread}\) . The paper is not focused on characterisation of the carbon fibres resistivity, \(\:{\lambda\:}_{el-f}\) , as the suppliers typically provide the resistivity value of the carbon fibres. The total area of carbon fibres between electrodes \(\:{A}_{f}\) can be calculated as Eq. ( 4 ). $$\:{A}_{f}=\frac{{M}_{f}}{{\rho\:}_{f}*d}$$ 4 where \(\:{M}_{f}\) is the total mass of the fibres between the electrodes, \(\:{\rho\:}_{f}\) is the density of the fibres and \(\:d\) is the length of the conducting fibres between the electrodes. Similarly, \(\:{M}_{f}\) can be written in terms of the fibre areal weight of the carbon layer, \(\:{\omega\:}_{f}\) , as Eq. ( 5 ). $$\:{M}_{f}={\omega\:}_{f}*b*d$$ 5 where \(\:b\) is the width of the conducting CFRP and in longitudinal case is equal to the width of the electrodes if the electrode edges, parallel to the fibre direction, are perfectly aligned to each other. Substituting Eq. ( 5 ) in (4), we can rewrite the total carbon fibre cross sectional area based on the fibre areal weight as Eq. ( 6 ). $$\:{A}_{f}=\frac{{\omega\:}_{f}*b}{{\rho\:}_{f}}$$ 6 substituting Eq. ( 6 ) in (3), we derive $$\:{R}_{CFRP}=\:{\lambda\:}_{el-f}\frac{{\rho\:}_{f}}{{\omega\:}_{f}}\:\frac{d}{b}$$ 7 Equation ( 7 ) calculates the longitudinal CFRP resistance using carbon fibre properties (fibre resistivity and density), carbon layers fibre areal weight which is generally provided by the carbon prepreg manufacturers, the electrodes distance and the electrodes width. This is for the case where the electrodes widths are perfectly aligned, however when there is an offset between the two electrodes, \(\:b\) should be replaced with \(\:{b}_{overlap}\) (overlap width) as shown in Fig. 6 (d). This relationship is limited to the longitudinal resistance of a UD composite plate, which is predominant until full electrode width offset is reached. An offset beyond full electrode width means there is no longitudinal carbon fibre directly underneath the two electrodes and the transverse CFRP resistance of the carbon layer needs to be accounted. Length of the electrodes, L, does not appear in Eq. ( 7 ) suggesting it is not a controlling parameter in \(\:{R}_{CFRP}\) , however, electrodes length can affect \(\:{R}_{interface}\) and consequently \(\:{R}_{contact}\) and therefore, it is studied experimentally later in section 6.2 of this paper. 4 FINITE ELEMENT ANALYSIS To validate the assumptions made in Ohm's law and to predict the electrical resistance in a UD carbon fibre laminate with two surface electrodes, a 3D FE model is developed. Simulations are performed to evaluate the effects of different carbon layer thickness, electrode materials and electrode thickness on total resistance \(\:{R}_{Total}\) of the composite. FE can simulate non-uniform electrical current in CFRPs and therefore, it can help in accurately estimating the spread resistance \(\:{R}_{spread}\) . The modelled CFRP plates have dimensions of 100 mm along the fibre direction and 40 mm in transverse direction with two electrodes of, L, 10 mm long in the fibre direction, \(\:b\) , 20 mm wide in the transverse direction and the distance between the inner edges of the electrodes, \(\:d\) , is set to be 80 mm as schematically shown in Fig. 3 . A potential difference of 0.6 volts is applied to the electrodes and the total electrical current is read after the analysis is complete. The resistance is calculated by dividing the applied potential voltage difference to the output current. No interface resistance is considered in this analysis between the electrodes and the CFRP layer. The composite longitudinal resistivity, \(\:{\lambda\:}_{el-0}\) , is equal to 0.0425 Ωmm as calculated using the material datasheet presented in Table 1 . The composite transverse resistivity, \(\:{\lambda\:}_{el-90}\) , used for this model is experimentally found to be 355.7 Ωmm. The FE model is built using hexahedral elements type Q3D78 to simulate the electrical behaviour of the carbon fibre laminate. Different in-plane mesh sizes of 1.0 mm, 0.5 mm and 0.2 mm are used to determine their effect on the numerical results. In the thickness direction, five elements per CFRP layer are used to capture the non-uniform electrical current through the thickness. Given the thickness of each thin-ply is only 0.028 mm, the mesh in thickness direction has a size of only 0.0056 mm, which is also used for the other FE models explained in the following paragraphs. This evaluation is only made for the case of one carbon layer and copper electrodes with 20 microns thickness. To evaluate the role of interface resistance in the measured composite total resistance, another numerical model is created with a one-micron thickness layer between the bottom surface of the electrode and the top surface of the composite plate, having the same length and width as the electrode. This thin layer is modelled as an isotropic material, and different electrical resistivity is applied to it e.g. composite longitudinal resistivity (0.0425 Ωmm), composite transverse resistivity (355.7 Ωmm) and resin (1x10 11 Ωmm). Additionally, the spread resistance is studied by modelling different distances between electrodes for CFRP laminates with one, two and four thin-ply carbon layers (CL), hereafter referred to as 1CL, 2CL and 4CL. The electrical current density (ECD) is measured in the thickness direction at different distances from the inner edges of the electrode. Figure 4 shows the ECD in the thickness direction for different carbon layer thickness. The results indicate that close to the inner edge of the electrodes, the ECD is higher at the top of the CFRP layer because the electrode is in contact with the top surface of the CFRP layer. However, after a short distance of about 2 mm for 1CL and 6 mm for 4CL, the ECD becomes uniform throughout the thickness in all CFRP laminates. The thinner CFRP layer reaches a uniform ECD distribution at a shorter distance from the inner edge of the electrodes than thicker laminates. Several FE models of CFRP laminates with different electrode distances are simulated to find the composite total resistance, \(\:{R}_{Total}\) which are shown with blue curves in Fig. 5 (a-c). Additionally, the CFRP resistance, \(\:{R}_{CFRP}\) , between the two electrodes are shown with orange straight lines, is calculated using Ohm’s law assuming a uniform electrical current through the thickness. The FE results show that at short distances between the electrodes, the relationship between total resistance, \(\:{R}_{Total}\) , and distance between the electrodes, \(\:d\) , is non-linear and this is because the electrical current is not uniform through the thickness of the sample. However, the \(\:{R}_{Total}\) curves start to present a linear behaviour from distances larger than approximately 2 to 6 mm between the electrodes depending on the thickness of the CFRP layer. As shown earlier in Fig. 4 this is because the ECD becomes uniform through the thickness direction after about 2 to 6 mm distance. And after this minimum distance the slope of the \(\:{R}_{Total}\) curves is the same as the slope of the \(\:{R}_{CFRP}\) theoretical lines. Figure 5 (d) illustrates the spread resistance, \(\:2\times\:{R}_{spread}\) for each carbon laminate evaluated with two electrodes mounted on the top surface of the composite. The spread resistance is calculated as the difference between the total resistance \(\:{R}_{Total}\) from FE and the CFRP resistance \(\:{R}_{CFRP}\) from Ohm’s law. The spread resistance increases with the number of carbon layers. As it takes longer distances for the current to reach uniform distribution across the thickness in thicker CFRP laminates. The spread resistance for both electrodes, 2 \(\:{R}_{spread}\) , for the modelled CFRP laminates are found to be 0.153 Ω (1CL), 0.177 Ω (2CL) and 0.223 Ω (4CL) as shown in Table 3 . A separate FE model with the electrodes located at the edges of the carbon laminate, instead of being on top, has also been developed and the results are shown in Fig. 5 (c) with purple dots. This total resistance \(\:{R}_{Total}\) from the FE simulation is found to be exactly the same as the CFRP resistance, \(\:{R}_{CFRP}\) , which assumes uniform current in the sample cross-section. 5 Experiments 5.1 Materials All the experiments were conducted on UD thin-ply carbon fibre prepreg from SK Chemicals with the commercial name Skyflex USN020 with TC-33 carbon fibre and K51 epoxy resin system with a ply thickness of about 30 microns when cured. The fibre diameter is 7 microns, and the fibre areal weight is 20 gsm with a fibre volume fraction of 40% as specified in the manufacturer's data sheet. A single layer of S-glass prepreg, manufactured by Hexcel with 913 resin is added to the bottom of the CFRP laminate to enhance the stiffness and provide electrical insulation to avoid accidental contact with other conductive surfaces. As listed in Table 1 , different metal foils such as copper (Cu), brass and aluminium (Al) with varying thickness from 10 µm to 200 µm are used as electrodes to study the effect of electrode material and thickness. In addition, two conductive paints made of durable acrylic lacquer, one with nickel (Ni) particles and the other with silver (Ag) particles are also used as electrodes to compare them against the metal foil electrodes. Table 1 Electrical resistivity and density of the applied electrode materials in the experiments and the epoxy resin, TC-33 carbon and S-Glass fibres. Fibre, resin and electrode material Electrical resistivity (Ωm) Density (g/cm³) Tairyfil TC-33 carbon fibre a 1.73×10 − 5 1.80 Hexcel S-glass fibre b 4.02×10 10 2.48 Copper (Cu) 1.68×10 − 8 8.96 Brass 5.90–7.10×10 − 8 8.40–8.73 Aluminium (Al) 2.65×10 − 8 2.70 Nickel (Ni) paint c 6.80×10 − 5 1.51 Silver (Ag) paint d 0.50–1.25×10 − 6 1.70 Epoxy matrix ~ 10 13 1.10–1.40 a Obtained from Tairyfil product manufacturer data sheet. b Obtained from Hexcel product manufacturer data sheet. c Obtained from M.G. Chemicals product technical data sheet. d Obtained from Chemtronics product technical data sheet. 5.2 Manufacturing After cutting the copper, brass and aluminium foils to a desired rectangular size as required for the composite test specimens, they are rinsed in acetone and dried to remove any dust particles before being applied on the carbon fibre prepreg. Manufacture of the laminates is similar to standard composite curing procedures for prepreg layups. The carbon block comprising of one, two, or four carbon plies is stacked on top of the single glass layer. A non-stick template with stencil like cut outs is used on top of the carbon block to accurately mount the electrodes at the required locations on the CFRP laminate as presented in Fig. 2 . After positioning the metal foils, they are gently pressed by hand onto the prepreg layup to ensure secure placement once the non-stick template is removed, minimising variability in geometry and alignment across specimens. The use of a non-stick template ensures precise electrode placement, enhancing reproducibility in electrode integration across all manufactured CFRP plates. The conductive paint electrodes are drawn on the carbon fibre prepreg with a pen tip dispenser. The non-stick stencil guide is used to deposit sufficient electrode material onto the carbon prepreg arranged next to the metal foil electrodes as indicated in Fig. 6 (a). This manual painting process has less control over the exact shape and thickness of the final epoxy electrode. In addition to the copper foil electrodes, a copper tape electrode with conductive adhesive backing is also tested which was directly applied to the prepreg without rinsing in acetone. Before curing the sample a release agent is gently applied on the thicker electrodes shown in Fig. 6 (a), 100 and 200 microns foil top surface to repel or discourage resin build up. The composite plate specimen with all electrodes in place are then vacuum bagged and transferred to an autoclave for curing. The plates are cured in an autoclave for 90 minutes at 125° C and 7 bar pressure as recommended by Hexcel in the 913 epoxy resin data sheet. After curing the CFRP plate with all the different electrodes, individual specimens with two electrodes at either side are carefully cut from the composite plate, as shown schematically with the dash-lines in Fig. 6 . This process is repeated for the 15 plates manufactured having 1, 2 and 4 carbon layers. 5.3 Test plan and electrodes arrangement Effects of electrode material and geometrical variation on the measured longitudinal total electrical resistance is studied and factors that lead to a stable connection with low contact and interface resistance with CFRP are investigated. The longitudinal total resistance is independently measured for variation of electrodes with different (i) thickness (ii) length (iii) width offset and (iv) materials. Figure 6 schematically shows the electrode arrangements in the manufactured CFRP plates which are subsequently cut into individual specimens to examine the effect of these variables on the measured total resistance. The variation of electrodes is repeated for 1, 2 and 4 UD thin-ply carbon layers (1CL, 2CL and 4CL) with five repeats each, except for the length and width offset tests having three repeats. Table 2 summarises the experimental test plan for variation of electrode parameters. The width of all the electrodes used for testing is 20 mm except in the electrodes length test, which had a width of 10 mm as stated in Table 2 . Table 2 Experimental test plan to study the performance of embedded co-cured electrodes to establish a stable electrical contact with CFRP composites. Investigated electrode parameters Electrode materials Electrodes length Electrodes width Electrodes thickness Electrodes width offset Distance between electrodes No. of carbon layers Schematic representation L (mm) \(\:b\) (mm) T (µm) O (mm) \(\:d\) (mm) (CL) Thickness Copper, brass 10 20 10, 20, 30, 40 a , 50, 80 a , 100, 200 0 80 1, 2, 4 Figure 6 (a) and (b) Length Copper 2.5, 5, 10, 20, 30, 40, 50 10 15 0 20 1 Figure 6 (c) Width offset Copper 10 20 15 0, 4, 8, 12, 16 20 1, 2 Figure 6 (d) Materials Copper, brass, aluminium b , copper tape with conductive adhesive c , nickel paint d and silver paint d 10 20 10, 20, 30, 40 a , 50, 80 a , 100, 200 0 80 1, 2, 4 Figure 6 (a) a Only for copper (Cu). b Aluminium (Al) thickness is 12 µm. c Copper tape with conductive adhesive has a total thickness of 85 µm. d Thickness of nickel (Ni) paint and silver (Ag) paint was not controlled due to their paint nature. Schematics in Fig. 6 (a) show the arrangement of electrodes with different thickness and electrode materials used in this study. Figure 6 (b) provides side view of the individual specimen after it has been cut from the composite plate. To investigate the effect of electrode length on the total measured resistance, a separate composite plate is manufactured, as shown in Fig. 6 (c), with individual specimens cut out for testing. In practice, electrodes might have offset or misalignment which can affect the measured experimental resistance and therefore, studying offset between electrodes edges as shown in Fig. 6 (d) is also important. Tests are also conducted to investigate the influence of electrode material in contact with carbon fibres by studying the measured total resistance with different electrode materials set which include Cu, brass and Al foils as well as Ni paint and Ag paint as outlined in Table 2 . In addition to these electrode materials as shown in Fig. 6 (a), a Cu tape with conductive adhesive backing having a total thickness of 85 µm (35 µm Cu foil + 50 µm conductive adhesive) was also used, as the tape manufacturer claimed the conductive adhesive has better bonding. These electrodes set are later cut and sectioned for microscopy analysis to examine the fibre-electrode interface contacts. The micrographs are presented in section 6.4 optical microscopy results of co-cured electrodes. 5.4 Resistance measurement Two-point probe (2-pp) method using a standard handheld digital ohmmeter with an accuracy of ± 0.5–0.8% is used to measure the experimental total resistance. Results obtained from this was previously compared with resistance readings obtained using a NI-DAQ unit and the values were found to be within 0.5-1%. Devices like Kelvin clips are not required for use in this study. A four-point probe (4-pp) method which eliminates the contact resistance in its measurements is typically useful for measuring very low resistance values or in high contact resistance cases. However, the objective of this paper is not to characterise the electrical resistance of the CFRP layer but to study the performance of the embedded co-cured electrodes in providing a low contact resistance interface for the measuring probes. Therefore, the contact resistance needs to be included in the experimental measurements to assess if this technique can provide a stable low contact resistance connection. One common approach to measure the contact resistance and its constituents i.e. interface and spread resistance is to use two-point probes on several samples with varying distances between the electrodes to obtain results similar to our FE results in Fig. 5 . However, implementing this experimentally for the entire range of materials and configurations of interest would require significantly large number of tests. To address this, FE analysis as shown in Fig. 5 is used to estimate the spread based on varying distances between the electrodes and for the experiments, the distance between the electrodes is kept constant and the obtained values are compared against each other as well as the FE and the analytical results. This combined approach provides reliable insights into contact resistance between electrodes and carbon fibre in composite materials. All the tests conducted in this research measured the composite specimen resistance at room temperature. 5.5 Pull-off measurements to assess mechanical bonding of the co-cured electrodes The adhesion strength between the co-cured electrodes and the CFRP layers is measured using a portable adhesion testing unit, P.A.T handy (DFD® Instruments), in accordance with a modified version of ASTM-D4541-17. Steel stubs with 2.8 mm radius are adhesively bonded to the electrodes using DFD® E1100S epoxy, which is cured for 60 min at 140°C, and then left to cool to room temperature. Electrodes are cleaned with compressed air, and air bubbles formed between the stub and electrode are carefully removed through pressing of the stubs. Any excess epoxy following curing is removed via a cylindrical cutting tool supplied with the equipment. Load is applied hydraulically through 4 pins surrounding the stub, applying force against a ring between the electrode and tester, enabling even force distribution. Each of the stubs are then pulled-out vertically with a calibrated hydraulic pump until detachment. The adhesion strength is determined from the recorded failure value divided by the quantified detached surface area. Analysis of the failure sites was conducted using a JEOL 6490LV scanning electron microscope. For adhesion measurements, a modified standardised set up was employed due to the nature of the samples being tested. A stainless-steel plate was attached behind the CFRP to provide stability due to its flexibility. 6 RESULTS 6.1 Effect of autoclave curing Figure 7 shows variations in the measured total resistance before and after curing the composite laminate with copper electrodes of different thickness. In the uncured stage, a higher total resistance is observed as the electrodes are not embedded in the composite. Instead, they are firmly pressed down by hand into the prepreg laminate and subsequently the uncured total resistance is recorded. Hence, the uncured total resistance values are susceptible to large variations, as shown by the large scatter in the error bars in Fig. 7 . It is evident that uncured total resistance is always significantly higher than cured total resistance and the theoretical CFRP resistance value. Therefore the contact resistance is high before the composite and electrodes are co-cured. After the laminate is cured, the electrodes are embedded in the composite to form a stable interface as shown in Fig. 13 micrograph and the cured total electrical resistance is close to the theoretical CFRP resistance found using Eq. ( 7 ). This demonstrates that co-curing electrodes along with carbon fibre prepreg with external pressure can significantly reduce the contact resistance. Furthermore, the average cured total resistance of the 4 carbon layers (4CL) specimens has a low scatter demonstrating the repeatability of the resistance measurements among different samples. 6.2 Electrodes geometrical variation Figure 8 shows the variation of the cured total resistance with respect to the copper electrodes thickness for three different CFRP layer thickness. The average measured cured total resistance values of 1CL, 2CL and 4CL specimens displayed in Fig. 8 are all close to their respective theoretical CFRP resistance values, especially for 1CL and 2CL specimens with electrode thickness between 20 and 200 microns. This indicates that the cured total resistance is largely independent of the electrode thickness. As per Eq. ( 1 ) the contact resistance value for a single electrode is calculated from the difference between the cured total resistance, \(\:{R}_{Total}\) , and the CFRP resistance, \(\:{R}_{CFRP}\) , divided by 2. In the case of 4CL samples the average contact resistance value is 0.31 Ω. This includes both interface resistance and spread resistance as highlighted in Eq. ( 2 ). Section 4 explains using FE analysis to calculate the spread resistance and for a single electrode contact in 4CL it is estimated to be 0.11 Ω as shown in Table 3 . This suggests that the average interface resistance for 4CL laminate is only 0.20 Ω. Similarly, for 1CL and 2CL laminates, the average contact resistance from the experiments is found to be 0.16 Ω and 0.14 Ω respectively. And from the subsequent FE analysis, the estimated spread resistance is 0.08 Ω (1CL) and 0.09 Ω (2CL). Therefore the average interface resistance for 1CL and 2CL equates to be 0.08 Ω and 0.05 Ω respectively. The average coefficient of variation (CV) of all 1CL, 2CL and 4CL samples are 5.1%, 3.7% and 6.7% respectively as provided in Table 3 . Therefore the results are deemed repeatable. Carbon fibres exhibit slight undulations, and it is widely accepted that these undulations cause individual fibres to come into contact with each other. This contact is responsible for electrical flow in the transverse direction. Varying the electrodes length examines whether there exists a minimum electrode length necessary to achieve this contact between the fibres and the electrodes. Figure 9 shows the effect of varying electrodes length in the fibre direction on the cured total resistance of one carbon layer specimens. Distance between the inner edges of the two copper electrodes \(\:d\) is kept constant and equal to 20 mm, as shown in Fig. 6 (c). The measured cured total resistance of the 1CL composite specimen shown in Fig. 9 are similar for all electrode lengths from 2.5 mm to 50 mm and are close to the theoretical CFRP resistance value. This suggests that copper electrodes with lengths as short as 2.5 mm still have a low interface resistance. The error bars show only a small variation of the resistance between different samples and hence the obtained results are consistent in establishing a good contact with carbon fibres in the CFRP layer. Figure 10 shows the cured total resistance against variation of electrodes width offset (O) in 1CL and 2CL specimens compared with their theoretical CFRP resistance calculated using Eq. ( 7 ) having overlapping width. Increasing the width offset O, increases the measured cured total resistance of the composite in both 1CL and 2CL specimens. This increase is driven by the reduction in the effective overlap width \(\:{b}_{overlap}\) of the longitudinally conducting carbon fibres between the two electrodes. Therefore, it increases the overall measured longitudinal total resistance which is compatible with the analytical Eq. ( 7 ). 6.3 Electrode material Figure 11 compares the effect of the electrode materials, i.e. copper and brass, on the cured total resistance, \(\:{R}_{Total}\) , with respect to their theoretical CFRP resistance, \(\:{R}_{CFRP}\) , in 1CL, 2CL and 4CL samples for varying thickness of electrodes. Only the average total resistance is shown, and the error bars are not displayed in Fig. 11 to maintain clarity. The coefficient of variation of both electrode material is shown in Table 3 . In electrodes with similar thickness, the copper electrodes always provide lower total resistance, \(\:{R}_{Total}\) , values and are closer to the theoretical CFRP resistance, \(\:{R}_{CFRP}\) , when compared against the brass electrodes. This response is consistent in all 1CL, 2CL and 4CL specimens. Also, the CV of results for copper electrodes are smaller than brass electrodes results as provided in Table 3 . Additionally, the average total resistance, \(\:{R}_{Total}\) , values for aluminium foil, Cu tape with conductive adhesive, nickel paint and silver paint are represented in Table 3 . These electrode materials result in a higher total resistance and CV compared to copper electrodes. Table 3 Average measured cured total resistance, \(\:{R}_{Total}\) , values of 1, 2 and 4 carbon layers CFRP specimens with different electrode materials. Electrode material CFRP specimen 1CL 2CL 4CL \(\:{R}_{CFRP}=\) 6.23 Ω – Ohm’s law \(\:{R}_{CFRP}=\) 3.11 Ω – Ohm’s law \(\:{R}_{CFRP}=\) 1.56 Ω – Ohm’s law \(\:2\times\:{R}_{spread}=\) 0.153 Ω – FE \(\:2\times\:{R}_{spread}=\) 0.177 Ω – FE \(\:{2\times\:R}_{spread}=\) 0.223 Ω – FE Total resistance \(\:{R}_{Total}\) (Ω) [CV%] Experiments Contact resistance \(\:2\times\:{R}_{contact}\) (Ω) Interface resistance \(\:2\times\:{R}_{interface}\) (Ω) Total resistance \(\:{R}_{Total}\) (Ω) [CV%] Experiments Contact resistance \(\:2\times\:{R}_{contact}\) (Ω) Interface resistance \(\:2\times\:{R}_{interface}\) (Ω) Total resistance \(\:{R}_{Total}\) (Ω) [CV%] Experiments Contact resistance \(\:2\times\:{R}_{contact}\) (Ω) Interface resistance \(\:2\times\:{R}_{interface}\) (Ω) Copper (Cu) 6.54 [5.1] 0.31 0.16 3.39 [3.7] 0.28 0.10 2.18 [6.7] 0.62 0.40 Brass 7.05 [7.4] 0.82 0.67 4.24 [ 10 ] 1.13 0.95 2.95 [ 12 ] 1.39 1.17 Aluminium (Al) 143.78 [63] 137.55 137.40 202.26 [87] 199.15 198.97 175.64 [84] 174.08 173.86 Cu tape with conductive adhesive 36.40 [44] 30.17 30.02 17.73 [91] 14.62 14.44 12.90 [61] 11.34 11.12 Nickel (Ni) paint 16.22 [48] 9.99 9.84 11.86 [46] 8.75 8.57 8.60 [55] 7.04 6.82 Silver (Ag) paint 7.00 [ 13 ] 0.77 0.62 3.46 [ 10 ] 0.35 0.17 2.88 [37] 1.32 1.10 All reported contact resistance in this table are for similar electrode surface area of 200 mm 2 rectangular electrodes of 20 mm width and 10 mm length. Table 3 shows 1CL, 2CL and 4CL specimens cured total resistance, \(\:{R}_{Total}\) , values of copper electrodes and brass electrodes averaged over all the thickness used in the study compared with the average, \(\:{R}_{Total}\) , values of Al foil, Cu tape with conductive adhesive, Ni paint and Ag paint electrode materials. The contact resistance \(\:2\times\:{R}_{contact}\) is calculated by subtracting the theoretical CFRP resistance, \(\:{R}_{CFRP}\) , from the experimentally measured total resistance, \(\:{R}_{Total}\) , as indicated in Eq. ( 1 ). Contact resistance can be affected by the area of the electrode. Since all electrodes presented in Table 3 have similar area, this is a representative comparison between the applied electrodes. Table 3 shows that copper electrodes on average provide the lowest contact resistance and the lowest CV in all carbon layer thicknesses. These values have been measured across different copper electrode thicknesses and the CV in each sample batch with similar electrode thickness would be even smaller than the values in Table 3 . The measured total resistance of Ag paint electrodes has a smaller CV with a lower contact resistance when compared with Ni paint, Cu tape with conductive adhesive and Al foil electrodes. 6.4 Optical microscopy of co-cured electrodes Figure 12 shows the electrode/carbon fibres interface after co-curing the electrodes and the carbon fibre prepreg, which creates close contacts between them at the interface. As highlighted in Fig. 12 (a), the copper foil electrode is observed to have dents around the carbon fibres. This evidence suggests that the copper electrode touches the top row carbon fibres and generate a good electrical contact. Microscopy of co-cured brass electrode shown in Fig. 12 (b) indicates that they have similar electrode/carbon fibres contact with fewer interface dents compared to the copper electrodes. However, in the copper tape with conductive adhesive there is a clear gap between the electrode and carbon fibres filled with the conductive adhesive as shown in Fig. 12 (c). Figure 13 (a) shows the edge of an embedded 10 microns copper electrode co-cured with two carbon layers composite specimen resulting in a smooth electrode flush at the top surface of the composite layer as shown in Fig. 13 (b). It can be observed that the edge of the copper electrode is inside the composite specimen and hence has been embedded well. Similar to Fig. 12 , the co-cured copper electrode is shown to have close electrode/carbon fibres contacts and dents at the interface. Figure 14 shows the fibre orientation angle of 2.9⁰ from the CFRP surface line in a co-cured specimen embedded with a brass electrode of 20 microns thickness. UD carbon fibre prepregs are known to have fibre mis-orientation angle of ± 2–3 degrees and waviness along the fibre direction [ 34 ]. This shows that the co-cured electrodes are not introducing a significantly larger misorientation and therefore, will not significantly compromise the mechanical properties of the composite layer. Figure 15 shows the nickel paint and silver paint electrodes at their respective electrode/carbon fibres interface. Figure 15 (a) exhibits a heterogenous texture of the nickel particles making up the electrode layer with micro pockets of polymer matrix in between. Figure 15 (b) displays silver particles forming a more homogenous electrode layer and therefore has a better contact with carbon fibres resulting in a lower contact and interface resistance. Hence the measured total resistance is closer to theoretical CFRP resistance when compared to nickel paint electrodes, as presented in Table 3 . 6.5 Pull-off test In a pull-off test, predominantly three modes of failure may occur: full interfacial failure of electrode/CFRP interface, partial interfacial failure of electrode/CFRP interface, and failure of the adhesive between the stub and electrode. Figure 16 shows typical SEM images and EDX maps of these three failure modes after test is carried out. For accurate measurement of the interfacial strength, full interfacial failure is preferred since one can ascertain the force required for failure of the bond between the electrodes and the CFRP beneath. Failure of the adhesive between the stub and electrode gives an indication that the force required to break the bond between the electrode and CFRP is in excess of the adhesive’s strength and therefore gives a lower bound to the strength of the bond between the electrodes and the carbon layer. To highlight the variance on electrode thickness, the copper electrodes with 20, 50, and 200 micron samples are tested as copper electrodes used in this paper have the lowest interface resistance. Since the standard (ASTM-D4541-17) was designed for flat, rigid, metal surfaces, a reduction in average adhesive strength, as stated within the defined standard, may be seen due to flexing/bowing of the substrate materials generating additional coating stresses thus resulting in premature failure (such as those used in this study). Table 4 Pull-off adhesion data demonstrating average failure strength of co-cured copper electrodes (n = 4). Additionally, the frequency of each failure mechanism has been detailed. Electrode sample Failure strength (MPa) Full electrode/CFRP interfacial failure Partial electrode/CFRP interfacial failure Electrode/stub adhesive failure Cu 20 µm 11.4 ± 3.7 0 4 0 Cu 50 µm More than 25.0 ± 3.3 0 0 4 Cu 200 µm More than 24.6 ± 2.6 0 0 4 Table 4 presents the obtained pull-off test results. The thickness of the electrode exhibits an effect, with the thicker electrodes exhibiting higher failure loads. Additionally, for the copper electrodes with thickness of 50 and 200 microns both exhibited purely adhesive failure at about 25 MPa as presented in Table 4 . This indicates that the bond strength between the electrode and the CFRP layer is higher than 25 MPa. Due to the failure of adhesive between the stub and electrode it has not allowed application of higher loads for the measurement of the precise bond strength between the electrode and the carbon layer. The 20 microns thick copper electrode samples exhibited partial failure of the electrode at about 11 MPa, indicating a lower failure strength compared to the thicker counterparts. 7 DISCUSSION Comparison shown in Fig. 8 between the longitudinal CFRP resistance, \(\:{R}_{CFRP}\) , and the experimentally measured cured total resistance, \(\:{R}_{Total}\) , demonstrates that the electrode co-curing technique provides a stable, repeatable and low electrical contact resistance, \(\:{R}_{contact}\) , with almost all copper electrodes especially those with a minimum thickness of 20 microns. These findings establish co-cured electrodes as a better alternative to post-cure methods, offering a simpler, more reliable solution for achieving stable electrical contact in CFRP composites without additional surface preparation or fibre damage. The FE modelling results helped estimating the spread resistance, \(\:{R}_{spread}\) , in different CFRP laminates with different carbon layer thickness which is found to noticeably contribute to the contact resistance, \(\:{R}_{contact}\) of the co-cured copper electrodes as described in Table 3 . Hence the interface resistance, \(\:{R}_{interface}\) , is found to be low in co-cured copper electrodes suggesting that they indeed achieve a robust electrical connection in CFRP composites. Figure 8 indicates no significant effect of electrodes thickness on the cured total resistance of the CFRP laminate. Whereas from Fig. 9 it can be noted that electrodes can be as short as 2.5 mm and still provide a good electrical contact with the carbon fibres. Using a copper sintering approach a contact resistance per unit electrode area of 9.3×10 − 3 Ωmm − 2 was observed [ 23 ]. Whereas sintering using silver nanoparticles resulted in an average contact resistance per unit electrode area of 3.66×10 − 3 Ωmm − 2 [ 24 ] and 4×10 − 3 Ωmm − 2 [ 25 ]. Although the electro-copper plating technique on carbon fibre composite led to a contact resistance per unit electrode area of 6.9×10 − 4 Ωmm − 2 [ 18 ], due to the complexity and hazardous nature of the process this method is not suitable for large structures. In this work, the average contact resistance per unit electrode area of the co-cured copper foil electrodes shown in Table 3 for 1CL, 2CL and 4CL specimens are 7.75×10 − 4 Ωmm − 2 , 7×10 − 4 Ωmm − 2 and 1.55×10 − 3 Ωmm − 2 respectively. The obtained contact resistance using the co-curing technique results in a very low interface resistance, lower or in the range of many other much more complicated electrode fabrication techniques. Since the electrodes are mounted on CFRP before curing the composite, the need for any surface preparations e.g. sanding, polishing or laser treatment is eliminated. Such treatments would be typically necessary if electrodes are applied to a cured composite specimen. It is observed from the gathered experimental total resistance data, \(\:{R}_{Total}\) , that the uncured total resistance measured before curing of a composite laminate is significantly higher than the theoretical CFRP resistance and also has a large scatter as depicted in Fig. 7 . During the autoclave curing process, as the temperature increases the thermoset resin in the prepreg changes from a gel form to a low viscosity medium. The vacuum and external pressure applied to the prepreg laminate at elevated temperature press the electrodes into the prepreg, embedding them in the CFRP laminate. It is worth mentioning that while manufacturing the samples, two of the specimens shown in Fig. 6 (a) went through failed curing cycles with no vacuum and external pressure, and the resulting electrodes had high contact resistance similar to the uncured total resistance shown in Fig. 7 . After a successful curing cycle, the cured total resistance measured are much lower with a low CV as described in section 6.2 and Fig. 8 . Figure 12 (a), (b) and Fig. 13 (a) show the interface having a direct electrode to carbon fibres contact. A smooth flush top CFRP surface is shown in Fig. 13 (b) therefore the co-cured electrodes are well bonded to the laminate. The performed pull-off measurements presented in Table 4 provide the interfacial strength of the co-cured electrodes and the failure modes are depicted in Fig. 16 . In electrodes with 50 and 200 micron thickness, the electrode/CFRP bond performed better than the epoxy used to glue the stub and electrode, meaning that the bond between electrodes and CFRP laminate has a minimum of about 25 MPa strength. The 20 micron copper electrodes provided an average tensile bond strength of 11.4 MPa which shows a relatively good lower bound for the bond between the electrode and CFRP, meaning the electrodes do not de-bond from the CFRP layers easily. Pull-off test results demonstrate that co-cured electrodes maintain sufficient mechanical bonding strength with the CFRP substrate, with misalignment angles remaining below 3° as shown in Fig. 14 . These findings confirm that the integration of embedded electrodes does not compromise the structural integrity of the composite, supporting their potential in advanced multifunctional materials. Use of metal foil electrodes provides a good degree of control on electrode shape, geometrical parameters and is easy to apply on carbon fibre prepregs. Microscopic images of the electrodes show them embedded well into the composite top layer and are fixed in place after curing. Reducing the electrode thickness may have its advantages to minimise fibre misalignment and any impact on mechanical properties of the composite, however our results show that thicker electrodes exhibit higher bond strength with the CFRP layer. In this study, copper electrode with the thickness of 20 microns provided minimal interface resistance, \(\:{R}_{interface}\) , with acceptable bond strength to the composite layer. The experimental results in Table 3 show that the copper tape with conductive adhesive backing gives higher contact resistance compared with bare surface copper electrodes. Therefore, having a conductive glue layer on the copper foil hinders the achievement of a good electrical contact between the electrodes and the CFRP laminate. Due to the paint form at the time of application, it is more difficult to control the shape and size of both nickel paint and silver paint electrodes shown in Fig. 15 . When these paints are applied to carbon fibre prepregs before curing, particles are observed to seep through the carbon ply. Additionally, they require 20 to 30 minutes drying time to avoid surface spreading while bagging the composite laminate for autoclave processing. Hence conductive paints are less favourable electrodes and are more challenging to maintain repeatability. Aluminium electrodes have the highest contact resistance of all the tested materials. This is deemed to be due to oxidation of aluminium surface [ 35 ] which is electrically insulating and quickly forms around the metal and cannot be washed with acetone. From Table 3 it is clear that the cured total resistance, \(\:{R}_{Total}\) , of samples with aluminium electrodes are significantly higher than that of brass electrodes, however we know that resistivity of brass is higher than resistivity of aluminium as noted in Table 1 . Similarly we can see that total resistance, \(\:{R}_{Total}\) , of samples with brass electrodes are higher than that of silver paint electrodes, whereas the resistivity of silver paint is much higher than that of brass. Additionally, the resistivity of copper is less than half that of aluminium, however the achieved contact resistance value using the co-cured aluminium electrodes is several magnitudes higher than co-cured copper electrodes. Furthermore, as listed in Table 1 the resistivity of nickel paint is an order of magnitude higher than silver paint, this is a contributing factor in the higher contact resistance observed in nickel paint electrodes as compared in Table 3 and Fig. 15 with the heterogenous composition of the nickel particles. These results indicate that several factors e.g. surface topography, contact pressure, material property and chemical conditions at the contacting surfaces in addition to electrode material resistivity can affect the value of interface resistance, \(\:{R}_{interface}\) , and consequently the contact resistance, \(\:{R}_{contact}\) , between the CFRP and electrodes. From the FE analysis the CFRP resistance found for 1CL, 2CL and 4CL are 5.9 Ω, 3.3 Ω and 1.6 Ω respectively. The total composite resistance for the models without the 1-micron interface between electrodes and the CFRP layers were exactly the same when the longitudinal and transverse resistivity values were applied to the 1-micron interface layer. However, the results showed a significantly higher resistance of 1E6 Ω when resin resistivity was applied. Since the experimental total resistance are much lower than such values, and quite close to the theoretical CFRP resistance, it can be noted that a good contact between carbon fibres and electrodes has been achieved experimentally. Otherwise, a slight separation of 1 micron between fibres and electrodes could lead to much higher experimental resistance measurements. 8 CONCLUSIONS This study systematically evaluates how key electrode parameters influence the contact resistance in CFRP composites, establishing co-curing as a practical and non-invasive technique for embedding electrical connections. This paper demonstrates a non-invasive and simple electrode manufacturing technique to establish a reliable low-contact and interface resistance electrical connection with carbon fibres in CFRP composites. Most existing methods used in establishing electrical contact are based on applying the electrodes to cured composite specimens. This typically involves surface preparation that can introduce damage to the composite and the carbon fibres. These methods can be expensive, laborious, time consuming, and complex to execute. Co-curing thin metal foil or conductive paint electrodes on CFRP facilitates direct electrode/fibres contact without any fibre damage or the need for any additional fabrication stages e.g. surface preparation or extra curing cycles. The experimental results show a small scatter in the cured total resistance, \(\:{R}_{Total}\) , using copper foil electrodes with the lowest contact resistance per unit electrode area of 7×10 − 4 Ωmm − 2 . The spread resistance, \(\:{R}_{spread}\) , obtained from FE simulation has a sizeable contribution in the total contact resistance, \(\:{R}_{contact}\) , experimentally observed between the measuring copper electrodes and the CFRP. This contribution of the spread resistance infers that the influence of interface resistance, \(\:{R}_{interface}\) , is low in the co-cured copper electrodes. This study provides an accessible, low-cost, and practical approach for integrating electrical connections into CFRP composites. These results have implications for the design of multifunctional materials in aerospace, automotive, and energy sectors, where robust electrical performance is critical. Specific findings from this study are summarised below: Effect of electrodes material: co-cured copper foil electrodes have the lowest contact and interface resistance, followed by silver paint, brass foil, nickel paint and Cu tape with conductive adhesive. Silver paint forms a relatively homogenous continuous electrode layer and has a lower contact resistance than nickel paint electrodes. Aluminium electrodes have the highest contact resistance. Electrodes thickness: the thickness variation in copper foil electrodes from 20 microns upwards does not affect the measured cured total resistance and has consistently low contact and interface resistance values. A slightly higher contact resistance was observed for the foils with a thickness of 10 microns. Electrodes length: a variation of copper electrodes length greater than 2.5 mm has no tangible effect on the interface resistance. Electrodes width offset: increasing the width offset between the two electrodes decreases the total effective width (overlap width), thereby increasing the measured total resistance. The change in the resistance follows Eq. ( 7 ) up to an offset close to the electrode's width. Curing cycle: the measured uncured total resistance is significantly higher than the cured and theoretical CFRP resistance. The CFRP curing cycle requires an active vacuum and external pressure to achieve a uniform electrode and carbon fibre interface with low contact resistance. Declarations Author Contribution S.A.M. (Sheik Abdul Malik) conducted the manufacturing, experimental work, validation, methodology, investigation, formal analysis, and conceptualisation. S.A.M. also prepared the original draft of the manuscript.M.J. (Meisam J.) provided guidance on the experimental design, contributed to the investigation, formal analysis, and conceptualisation, and reviewed and edited the manuscript.M.D.W. (Matthew D. W.) performed the pull-off tests and analysis and contributed to writing and editing.J.D.A. (Jose D. A.) conducted the FE simulations and contributed to writing and editing.R.M.F. (Reda M. 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J. Mech. Sci. , vol. 124–125, no. January, pp. 37–47, (2017). 10.1016/j.ijmecsci.2017.02.026 Slade, P.G.: Electrical Contacts: Principles and Applications , Second Edi. CRC Press, (2014). 10.1201/b15640 Yu, H., Heider, D., Advani, S.: A 3D microstructure based resistor network model for the electrical resistivity of unidirectional carbon composites. Compos. Struct. no. 134 , 740–749 (2015). 10.1016/j.compstruct.2015.08.131 Frank, R., Morton, C.: Comparative corrosion and current burst testing of copper and aluminum electrical power connectors. Fourtieth IAS Annu. Meet Conf. Rec 2005 Ind. Appl. Conf. no. 1 , 442–447 (2005). 10.1109/IAS.2005.1518345 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Jun, 2025 Read the published version in Applied Composite Materials → Version 1 posted Editorial decision: Revision requested 12 Feb, 2025 Reviews received at journal 03 Feb, 2025 Reviews received at journal 19 Jan, 2025 Reviewers agreed at journal 19 Jan, 2025 Reviewers agreed at journal 15 Jan, 2025 Reviewers agreed at journal 15 Jan, 2025 Reviewers agreed at journal 06 Jan, 2025 Reviewers invited by journal 22 Dec, 2024 Editor assigned by journal 15 Dec, 2024 Submission checks completed at journal 15 Dec, 2024 First submitted to journal 13 Dec, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5639196","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":402887184,"identity":"14a42536-d3bd-4818-b21c-1e9f93548b7a","order_by":0,"name":"Sheik Abdul Malik","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIie2RsUrEMBjH/yGQW4q3Vir0FVKEA/GOvspXCnU5EHE5t4JQl4BrwJdwcjYU+gyFiBz4AndbxcXmwOGGaEeH/JaQwI/vFz4gEPiPxICpx/OEC7b9eXHIPxXBBZcgIJqisIMCIeJJSvp0b4zGSypmorr7HN7TPKnZbkB77lPkW0fmGTZruOhsRLeZOnvlpwrtwqvEa2m2sKzhs8aCiKmYkADt0humr3dOyZ1yMxDlo8K/flPQr+HCCheGiKgYFeGm+MP6ShotbTkqZRJVVKq+aC6UvPJ+P9Xlx15t7Opx3mX7YUmrB122/bC5zGpv2WHW0c3tyb/IQCAQCEzgG9QnU2sNWwZXAAAAAElFTkSuQmCC","orcid":"","institution":"University of Strathclyde","correspondingAuthor":true,"prefix":"","firstName":"Sheik","middleName":"Abdul","lastName":"Malik","suffix":""},{"id":402887185,"identity":"d868df65-bfac-4eed-b5e3-23320f9638bf","order_by":1,"name":"Meisam Jalalvand","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Meisam","middleName":"","lastName":"Jalalvand","suffix":""},{"id":402887186,"identity":"46172c16-0aa4-491e-902a-11beb6049fd4","order_by":2,"name":"Matthew D. Wadge","email":"","orcid":"","institution":"University of Nottingham","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"D.","lastName":"Wadge","suffix":""},{"id":402887187,"identity":"a03f0c28-e7f1-420b-9075-bfcd222eaa3d","order_by":3,"name":"J. D. Acosta","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"J.","middleName":"D.","lastName":"Acosta","suffix":""},{"id":402887188,"identity":"a79f5bd6-b4f6-4a78-b7fc-c7c99996297c","order_by":4,"name":"Reda M. Felfel","email":"","orcid":"","institution":"University of Strathclyde","correspondingAuthor":false,"prefix":"","firstName":"Reda","middleName":"M.","lastName":"Felfel","suffix":""}],"badges":[],"createdAt":"2024-12-13 15:23:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5639196/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5639196/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10443-025-10345-1","type":"published","date":"2025-06-19T15:57:09+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":74079930,"identity":"20124bde-8d4b-4571-9b79-e86898d9a80e","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":306375,"visible":true,"origin":"","legend":"\u003cp\u003eDifferent techniques used for electrode fabrication on CFRP specimens.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/4fe78f5dc02bdecde11a5168.png"},{"id":74079911,"identity":"ea8eef11-5ff5-40b9-a747-797f7a848050","added_by":"auto","created_at":"2025-01-17 14:16:34","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":196885,"visible":true,"origin":"","legend":"\u003cp\u003eConcept of co-curing electrodes directly on a CFRP specimen.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/e1a592be381c4631051d0905.png"},{"id":74079924,"identity":"846afa22-df77-4ece-8b46-1c0c801bda02","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":71757,"visible":true,"origin":"","legend":"\u003cp\u003eComposite laminate with embedded electrodes showing the geometrical parameters used to calculate CFRP resistance.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/690004f6279d7ed17202db31.png"},{"id":74079926,"identity":"af50f3c1-104c-459e-832d-467cd91dfdb3","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":142911,"visible":true,"origin":"","legend":"\u003cp\u003eFE simulation results of electrical current density in the thickness direction at different distances from the inner edge of the left electrode (a) 1CL, (b) 2CL and (c) 4CL.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/6744bc2e60a6ee60e59e8813.png"},{"id":74081027,"identity":"0e6a2f67-cf76-4f03-bdb9-b0095fd3706f","added_by":"auto","created_at":"2025-01-17 14:24:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":188080,"visible":true,"origin":"","legend":"\u003cp\u003eFE simulation results of electrical resistance at different distances between electrodes d for (a) 1CL, (b) 2CL and (C) 4CL (d) Spread resistance.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/6b51d4d3c34c142eb2528680.png"},{"id":74079916,"identity":"aa493e29-6f70-4c6f-8e9a-daa47146fc44","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":920025,"visible":true,"origin":"","legend":"\u003cp\u003eElectrodes arrangements for the experimental campaign showing (a) variation of electrodes thickness and material (b) thickness side view of individual sample electrodes set cut out from the plate (c) variation of electrodes length and (d) variation of electrodes width offset.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/c0aeb000da47b4ad8b9dd683.png"},{"id":74079929,"identity":"a16bcd85-8e2d-4946-a81d-cf5753d5d480","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":221049,"visible":true,"origin":"","legend":"\u003cp\u003eUncured and cured total resistance compared with the theoretical CFRP resistance of 4 carbon layers specimens having varying electrode thickness.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/35619c0db7ae5aad47bb75e1.png"},{"id":74081018,"identity":"808060b1-d4cd-4c80-8d14-914840df3a69","added_by":"auto","created_at":"2025-01-17 14:24:35","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":261656,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of copper electrodes thickness comparing cured total resistance (R\u003csub\u003eTotal\u003c/sub\u003e) with theoretical CFRP resistance (R\u003csub\u003eCFRP\u003c/sub\u003e) of 1, 2 and 4 carbon layers specimens.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/fa6a7e01f5e13b420973a193.png"},{"id":74079922,"identity":"f51950e0-8ac0-407c-aae6-c447624e288a","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":150920,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of electrodes length comparing cured total resistance (R\u003csub\u003eTotal\u003c/sub\u003e) with theoretical CFRP resistance (R\u003csub\u003eCFRP\u003c/sub\u003e) of 1 carbon layer specimens.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/17afe9245d1575ac936d86a8.png"},{"id":74081019,"identity":"bad7cbf0-ce3b-42dc-9a3b-b9bb81837c9d","added_by":"auto","created_at":"2025-01-17 14:24:35","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":334481,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of electrodes width offset comparing cured total resistance (R\u003csub\u003eTotal\u003c/sub\u003e) with the overlapping width theoretical CFRP resistance (R\u003csub\u003eCFRP\u003c/sub\u003e) of 1 and 2 carbon layers specimens.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/b6165bf6b5758a7f36fd26f1.png"},{"id":74079943,"identity":"f7b88764-e1c2-4d40-b7ac-521d300dc088","added_by":"auto","created_at":"2025-01-17 14:16:36","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":290121,"visible":true,"origin":"","legend":"\u003cp\u003eCured total resistance (R\u003csub\u003eTotal\u003c/sub\u003e) as a function of electrodes thickness for brass and copper electrode material compared with theoretical CFRP resistance (R\u003csub\u003eCFRP\u003c/sub\u003e) of 1, 2 and 4 carbon layers specimens.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/475e7b22241204cd09911af7.png"},{"id":74079910,"identity":"6f43ece2-5d83-4aa4-9333-8b447588f9d5","added_by":"auto","created_at":"2025-01-17 14:16:34","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":102014,"visible":true,"origin":"","legend":"\u003cp\u003eMicroscopic image of the co-cured (a) copper foil electrode showing foil dents at the interface and the adjacent carbon fibres (b) brass foil electrode and (c) copper tape with conductive adhesive.\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/ad6f23220e318c84f9fa9b2e.png"},{"id":74079917,"identity":"86a2e8c3-2855-4a66-834f-5336c17eaec8","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":92047,"visible":true,"origin":"","legend":"\u003cp\u003eComposite specimen showing (a) microscopic image of the edge of an embedded co-cured copper electrode contact interface with the carbon fibres and (b) top view of the cured specimen with electrode flush top surface.\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/17a7fa9cb078c1fc531a2791.png"},{"id":74079936,"identity":"30726760-2391-43e2-ae5e-060c6b342412","added_by":"auto","created_at":"2025-01-17 14:16:36","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":75151,"visible":true,"origin":"","legend":"\u003cp\u003eLongitudinal section microscopic image of the co-cured CFRP specimen with brass electrode showing the fibre orientation angle.\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/157dd44fc5edc7e916ab567e.png"},{"id":74079923,"identity":"5e603e57-a5c6-467a-b042-6dede7867116","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":157859,"visible":true,"origin":"","legend":"\u003cp\u003eMicroscopic images of the co-cured (a) nickel paint and (b) silver paint electrodes.\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/6452d27d9f38c38980f18bde.png"},{"id":74079921,"identity":"2035bde4-1c24-4f38-bfec-340ad45e7e3e","added_by":"auto","created_at":"2025-01-17 14:16:35","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":96247,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentative failure modes of samples within this study to illustrate full, partial and adhesive failure.\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/d4d32ff225223d1f0c4d869e.png"},{"id":85231287,"identity":"08329a3c-f5a7-4341-b7a6-1be1155ad33d","added_by":"auto","created_at":"2025-06-23 16:04:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4915540,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5639196/v1/b804782d-303e-468a-9166-d58dd0f5ded6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eRobust Electrical Contact With Low Interface Resistance Using Embedded Co-cured Electrodes in Carbon Fibre Composites\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eFor decades, researchers have studied the self-sensing functionalities of carbon fibre composites for various structural health monitoring approaches. Such studies have typically included monitoring the health of a structure in real time using resistance measurements to develop damage detection and early warning capabilities [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Any change in resistance of carbon fibre reinforced polymer (CFRP) laminates has been reported to indicate the development of internal damages, e.g. fibre breakages or delamination. Furthermore, studies have evaluated CFRP in various loading conditions and the feasibility of using the electric resistance change method to assess the structural integrity of composite materials while in service [\u003cspan additionalcitationids=\"CR4 CR5 CR6\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. These methods highlight the need to accurately capture CFRP resistance measurements directly linked to the physical changes within the material to infer practical sensory applications.\u003c/p\u003e \u003cp\u003eTypically, it is difficult to establish good electrical contact between carbon fibres in composites and external sources of electrical power as fibres are embedded in a polymer matrix. This can result in high 'apparent electrical resistance' being observed. This apparent high contact resistance is caused by the matrix acting as a barrier impeding a good electrical continuity. This issue can be addressed using a conductive intermediary material known as electrode, which is applied to bridge the connection between carbon fibres and the external source of electrical power. The primary function of an electrode is to provide a uniform and stable connection with an external electrical source, e.g. measuring probes to determine the resistance of the system. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarises different electrode fabrication techniques grouped into two main categories: (i) electrodes co-cured along with the CFRP composite and (ii) electrodes manufactured on cured composite following surface preparation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSeveral studies have experimented introducing electrodes on cured CFRP specimens using various complex and expensive fabrication techniques. These include methods like conductive metal foil with applied external pressure [\u003cspan additionalcitationids=\"CR9 CR10 CR11 CR12 CR13\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], conductive paints [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], electrolytic deposition or electroplating [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] sputtering [\u003cspan additionalcitationids=\"CR20 CR21\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], sintering [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u0026ndash;[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] and soldering [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. All of these methods require different forms of extensive surface preparation as a first stage to remove the insulating matrix layer, before applying the electrode material to the carbon layer, which is time consuming, need specialist facilities and is labour intensive.\u003c/p\u003e \u003cp\u003eThe most common surface preparation step employed is surface sanding, grinding or the use of a laser [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In addition to mechanical polishing, sample surface edges undergoing chemical polishing have also been reported [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Sanding usually involves rigorous manual abrasion carried out using sandpaper (SiC-paper grit 320 to 1000) followed by polishing and the specimen is cleaned afterwards with acetone to remove debris particles. Sanding the CFRP surface can often lead to non-repeatable results, damage to carbon fibres and variability in different specimens. After sanding and polishing the surface Laudani et al. used copper tapes and secured it using conductive silver paint [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. In addition, they applied 20 MPa pressure on the metal electrodes through a hydraulic press to mitigate the effects of surface roughness and improve the ohmic contact. Many studies have used copper strips or foils mechanically held by plastic grips [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], screw actuator [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], magnetic nails [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], bench vice [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] or springs [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] to apply pressure on the electrodes to improve the contact between the electrodes and CFRP to aid reproducibility of the measured electrical resistance. These special arrangements to promote direct electrode contact with carbon fibre are not straightforward and is not practical in real use case scenarios.\u003c/p\u003e \u003cp\u003eContact resistance (CR) between electrodes and CFRP laminates comprises two key elements: interface resistance (IR) and spread resistance (SR). Interface resistance determines the electrical current flow across the boundary between the electrodes and the CFRP laminate. Factors such as surface roughness, oxide layers, imperfect contact, material property mismatch and surface contamination contribute to interface resistance. Whereas, spread resistance arises due to the finite size of the contact area between metallic foils and CFRP composites. It reflects how easily current can spread through the CFRP laminate. The arrangement and configuration of electrodes significantly impacts spread resistance, however these aspects do not affect the resistance at the interface between the electrode and CFRP laminate. For instance, edge electrodes applied to the full edges of a CFRP laminate exhibit minimal spread resistance because the current is already evenly distributed through the thickness. However, a surface electrode is only in contact with surface carbon fibres, and therefore experiences non-negligible spread resistance. In this case, the current introduced at the sample\u0026rsquo;s surface must navigate a restricted area before evenly spreading through the CFRP laminate\u0026rsquo;s thickness. In the literature, the interface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e and spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e, are not separately discussed and only the contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e, in electrodes applied post curing of the CFRP have been reported using different techniques [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This information is not quantitatively reported for co-cured electrodes.\u003c/p\u003e \u003cp\u003eCo-curing rectangular copper foil electrodes [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], using flexible printed circuit boards [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and embedding conductive wires [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] during the composite lay-up stage of a CFRP specimen to achieve electrical connection have been used in cases for damage detection. To the authors\u0026rsquo; best knowledge, no paper has individually studied the co-curing technique in itself detailing its ability to achieve a stable, reproducible, and low contact resistance electrical connection in CFRP composites. With electrodes being applied to the top surface of prepregs before curing the composite, the need for surface preparation and the risk of surface damage is eliminated. Different parameters such as electrodes thickness, length, width offset, material, and the CFRP fibre areal weight are examined in this paper to understand their effects on the contact resistance and more specifically on interface resistance. Finite element (FE) method is used to estimate spread resistance in different CFRP layers with varying thickness. This allows to calculate the interface resistance between the electrodes and CFRP laminates from the experimental contact resistance results. These aspects have not been studied previously and are important in informing the optimal electrode geometry parameters. This paper integrates FE analysis and experimental validation to quantify the effects of electrode geometry, material, and alignment on both electrical and mechanical performance.\u003c/p\u003e"},{"header":"2 Concept","content":"\u003cp\u003eElectrode materials are applied on the uncured CFRP prepregs and then co-cured together under pressure and heat as shown schematically in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The matrix is not solidified at early stages of the curing cycle and the external pressure applied in autoclave can press the electrodes into the CFRP. This increases the possibility of achieving a good contact between the carbon fibres and the electrode before the matrix is set. After completion of the curing cycle, the electrodes are embedded in the carbon fibre layer with a flush top surface. Attaching probes on these electrodes will establish the electrical connection needed for monitoring systems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this paper, two co-cured electrode concepts are tested: (i) electrically conductive metal foil and (ii) thermosetting conductive paint. This technique does not require any surface post processing after the composite is cured. It is significantly easier, robust and lower cost compared to those fabrication processes that apply electrodes to the composite after curing. The post-cure methods often involve energy-intensive processes and can lead to material wastage due to surface preparation steps. In contrast, the co-curing technique simplifies electrode integration, reducing energy consumption and minimising material waste, thereby offering a more sustainable alternative for large-scale manufacturing. This makes it particularly suitable for high-performance applications such as aerospace, automotive, and energy systems, where both reliability and cost-efficiency are critical.\u003c/p\u003e"},{"header":"3 Contact resistance and CFRP resistance","content":"\u003cp\u003eThe longitudinal electrical resistivity of CFRP composites along the fibre direction is significantly lower than the transverse resistivity and through-thickness resistivity [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. This paper is focused on the longitudinal resistance of unidirectional (UD) CFRPs and the effects of electrodes on the measured resistance. The experimentally measured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e of the composite has a non-zero contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e at each of the two measuring electrodes that is added to the theoretical CFRP resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This equation assumes a uniform current distribution in the thickness direction, providing a simplified framework for calculating longitudinal resistance and is validated using FE simulations as explained later.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{R}_{Total}={R}_{CFRP}+\\:2\\times\\:{R}_{contact}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e, has two elements as shown in (2).\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{R}_{contact}=\\:{R}_{interface}+{R}_{spread}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eInterface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e, is the electrical resistance that arises at the interface between the electrode and the adjacent carbon fibres. The second factor is the spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e, which arises when current flows from a small contact area into a larger region of the bulk material. As the current spreads out from the confined contact area into the larger bulk, it encounters resistance due to the constrained flow paths and current crowding effects [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn an ideal case if the electrodes contact have zero interface resistance, and if the electrical current is uniformly spread between the two electrodes having zero spread resistance, the measured total resistance of the composite would be equal to the CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\:\\)\u003c/span\u003e\u003c/span\u003e= \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e. With a low contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e would be close but not exactly equal. CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, is the resistance between the electrodes if the current is uniform. Using Ohm's law of electrical resistance, the CFRP resistance can be written as Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) to estimate the longitudinal fibre direction resistance of the composite.\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{R}_{CFRP}=\\:{\\lambda\\:}_{el-0}\\:\\frac{d}{{A}_{c}}={\\lambda\\:}_{el-f}\\:\\frac{d}{{A}_{f}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{el-0}\\)\u003c/span\u003e\u003c/span\u003e is the fibre-direction CFRP electrical resistivity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is the shortest distance between the inner edges of the two electrodes as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{c}\\)\u003c/span\u003e\u003c/span\u003e is the total cross-sectional area of the CFRP between the two electrodes. Only the carbon fibres are the conductive medium and the polymer matrix has a significantly higher resistivity. Therefore, it is possible to estimate the CFRP resistance based on the resistivity of the carbon fibres, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{el-f}\\)\u003c/span\u003e\u003c/span\u003e and the total area of all the carbon fibres between the two electrodes, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{f}\\)\u003c/span\u003e\u003c/span\u003e, as shown in the right-hand side of Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe electrodes used in this research have a thin rectangular flat shape with resistance values significantly lower than that of composite. Hence, in Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) it is assumed that the apparent resistance between two electrodes in the fibre direction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, is independent of where the probes of the ohm meter touch the electrodes. This has been confirmed using the FE analysis as will be explained later. The analytical equations for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e provide the lowest possible electrical resistance between two surface electrodes as it assumes a uniform current between the electrodes. Non-uniform electrical current due to current spreading in the thickness direction increases the total electrical resistance between the electrodes and is accounted for in the spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e. The paper is not focused on characterisation of the carbon fibres resistivity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{el-f}\\)\u003c/span\u003e\u003c/span\u003e, as the suppliers typically provide the resistivity value of the carbon fibres.\u003c/p\u003e \u003cp\u003eThe total area of carbon fibres between electrodes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{f}\\)\u003c/span\u003e\u003c/span\u003e can be calculated as Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{A}_{f}=\\frac{{M}_{f}}{{\\rho\\:}_{f}*d}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{M}_{f}\\)\u003c/span\u003e\u003c/span\u003e is the total mass of the fibres between the electrodes, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{f}\\)\u003c/span\u003e\u003c/span\u003e is the density of the fibres and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is the length of the conducting fibres between the electrodes. Similarly, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{M}_{f}\\)\u003c/span\u003e\u003c/span\u003e can be written in terms of the fibre areal weight of the carbon layer, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}_{f}\\)\u003c/span\u003e\u003c/span\u003e, as Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{M}_{f}={\\omega\\:}_{f}*b*d$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:b\\)\u003c/span\u003e\u003c/span\u003e is the width of the conducting CFRP and in longitudinal case is equal to the width of the electrodes if the electrode edges, parallel to the fibre direction, are perfectly aligned to each other. Substituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) in (4), we can rewrite the total carbon fibre cross sectional area based on the fibre areal weight as Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{A}_{f}=\\frac{{\\omega\\:}_{f}*b}{{\\rho\\:}_{f}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003esubstituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) in (3), we derive\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{R}_{CFRP}=\\:{\\lambda\\:}_{el-f}\\frac{{\\rho\\:}_{f}}{{\\omega\\:}_{f}}\\:\\frac{d}{b}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eEquation (\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) calculates the longitudinal CFRP resistance using carbon fibre properties (fibre resistivity and density), carbon layers fibre areal weight which is generally provided by the carbon prepreg manufacturers, the electrodes distance and the electrodes width. This is for the case where the electrodes widths are perfectly aligned, however when there is an offset between the two electrodes, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:b\\)\u003c/span\u003e\u003c/span\u003e should be replaced with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{overlap}\\)\u003c/span\u003e\u003c/span\u003e (overlap width) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (d). This relationship is limited to the longitudinal resistance of a UD composite plate, which is predominant until full electrode width offset is reached. An offset beyond full electrode width means there is no longitudinal carbon fibre directly underneath the two electrodes and the transverse CFRP resistance of the carbon layer needs to be accounted. Length of the electrodes, L, does not appear in Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) suggesting it is not a controlling parameter in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, however, electrodes length can affect \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e and consequently \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e and therefore, it is studied experimentally later in section 6.2 of this paper.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"4 FINITE ELEMENT ANALYSIS","content":"\u003cp\u003eTo validate the assumptions made in Ohm's law and to predict the electrical resistance in a UD carbon fibre laminate with two surface electrodes, a 3D FE model is developed. Simulations are performed to evaluate the effects of different carbon layer thickness, electrode materials and electrode thickness on total resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e of the composite. FE can simulate non-uniform electrical current in CFRPs and therefore, it can help in accurately estimating the spread resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e. The modelled CFRP plates have dimensions of 100 mm along the fibre direction and 40 mm in transverse direction with two electrodes of, L, 10 mm long in the fibre direction, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:b\\)\u003c/span\u003e\u003c/span\u003e, 20 mm wide in the transverse direction and the distance between the inner edges of the electrodes, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e, is set to be 80 mm as schematically shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. A potential difference of 0.6 volts is applied to the electrodes and the total electrical current is read after the analysis is complete. The resistance is calculated by dividing the applied potential voltage difference to the output current. No interface resistance is considered in this analysis between the electrodes and the CFRP layer. The composite longitudinal resistivity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{el-0}\\)\u003c/span\u003e\u003c/span\u003e, is equal to 0.0425 Ωmm as calculated using the material datasheet presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The composite transverse resistivity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{el-90}\\)\u003c/span\u003e\u003c/span\u003e, used for this model is experimentally found to be 355.7 Ωmm.\u003c/p\u003e \u003cp\u003eThe FE model is built using hexahedral elements type Q3D78 to simulate the electrical behaviour of the carbon fibre laminate. Different in-plane mesh sizes of 1.0 mm, 0.5 mm and 0.2 mm are used to determine their effect on the numerical results. In the thickness direction, five elements per CFRP layer are used to capture the non-uniform electrical current through the thickness. Given the thickness of each thin-ply is only 0.028 mm, the mesh in thickness direction has a size of only 0.0056 mm, which is also used for the other FE models explained in the following paragraphs. This evaluation is only made for the case of one carbon layer and copper electrodes with 20 microns thickness. To evaluate the role of interface resistance in the measured composite total resistance, another numerical model is created with a one-micron thickness layer between the bottom surface of the electrode and the top surface of the composite plate, having the same length and width as the electrode. This thin layer is modelled as an isotropic material, and different electrical resistivity is applied to it e.g. composite longitudinal resistivity (0.0425 Ωmm), composite transverse resistivity (355.7 Ωmm) and resin (1x10\u003csup\u003e11\u003c/sup\u003e Ωmm).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAdditionally, the spread resistance is studied by modelling different distances between electrodes for CFRP laminates with one, two and four thin-ply carbon layers (CL), hereafter referred to as 1CL, 2CL and 4CL. The electrical current density (ECD) is measured in the thickness direction at different distances from the inner edges of the electrode. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the ECD in the thickness direction for different carbon layer thickness. The results indicate that close to the inner edge of the electrodes, the ECD is higher at the top of the CFRP layer because the electrode is in contact with the top surface of the CFRP layer. However, after a short distance of about 2 mm for 1CL and 6 mm for 4CL, the ECD becomes uniform throughout the thickness in all CFRP laminates. The thinner CFRP layer reaches a uniform ECD distribution at a shorter distance from the inner edge of the electrodes than thicker laminates.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSeveral FE models of CFRP laminates with different electrode distances are simulated to find the composite total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e which are shown with blue curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a-c). Additionally, the CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, between the two electrodes are shown with orange straight lines, is calculated using Ohm\u0026rsquo;s law assuming a uniform electrical current through the thickness. The FE results show that at short distances between the electrodes, the relationship between total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, and distance between the electrodes, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e, is non-linear and this is because the electrical current is not uniform through the thickness of the sample. However, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e curves start to present a linear behaviour from distances larger than approximately 2 to 6 mm between the electrodes depending on the thickness of the CFRP layer. As shown earlier in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e this is because the ECD becomes uniform through the thickness direction after about 2 to 6 mm distance. And after this minimum distance the slope of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e curves is the same as the slope of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e theoretical lines. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (d) illustrates the spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e for each carbon laminate evaluated with two electrodes mounted on the top surface of the composite. The spread resistance is calculated as the difference between the total resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e from FE and the CFRP resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e from Ohm\u0026rsquo;s law. The spread resistance increases with the number of carbon layers. As it takes longer distances for the current to reach uniform distribution across the thickness in thicker CFRP laminates. The spread resistance for both electrodes, 2\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e, for the modelled CFRP laminates are found to be 0.153 Ω (1CL), 0.177 Ω (2CL) and 0.223 Ω (4CL) as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. A separate FE model with the electrodes located at the edges of the carbon laminate, instead of being on top, has also been developed and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (c) with purple dots. This total resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e from the FE simulation is found to be exactly the same as the CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, which assumes uniform current in the sample cross-section.\u003c/p\u003e"},{"header":"5 Experiments","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Materials\u003c/h2\u003e \u003cp\u003eAll the experiments were conducted on UD thin-ply carbon fibre prepreg from SK Chemicals with the commercial name Skyflex USN020 with TC-33 carbon fibre and K51 epoxy resin system with a ply thickness of about 30 microns when cured. The fibre diameter is 7 microns, and the fibre areal weight is 20 gsm with a fibre volume fraction of 40% as specified in the manufacturer's data sheet. A single layer of S-glass prepreg, manufactured by Hexcel with 913 resin is added to the bottom of the CFRP laminate to enhance the stiffness and provide electrical insulation to avoid accidental contact with other conductive surfaces.\u003c/p\u003e \u003cp\u003eAs listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, different metal foils such as copper (Cu), brass and aluminium (Al) with varying thickness from 10 \u0026micro;m to 200 \u0026micro;m are used as electrodes to study the effect of electrode material and thickness. In addition, two conductive paints made of durable acrylic lacquer, one with nickel (Ni) particles and the other with silver (Ag) particles are also used as electrodes to compare them against the metal foil electrodes.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eElectrical resistivity and density of the applied electrode materials in the experiments and the epoxy resin, TC-33 carbon and S-Glass fibres.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFibre, resin and electrode material\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eElectrical resistivity (Ωm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eDensity (g/cm\u0026sup3;)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTairyfil TC-33 carbon fibre\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.73\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHexcel S-glass fibre\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.02\u0026times;10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCopper (Cu)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.68\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBrass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.90\u0026ndash;7.10\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.40\u0026ndash;8.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAluminium (Al)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.65\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNickel (Ni) paint\u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.80\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSilver (Ag) paint\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.50\u0026ndash;1.25\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEpoxy matrix\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e~\u0026thinsp;10\u003csup\u003e13\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.10\u0026ndash;1.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003ea\u003c/sup\u003e \u003cem\u003eObtained from Tairyfil product manufacturer data sheet.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003csup\u003eb\u003c/sup\u003e \u003cem\u003eObtained from Hexcel product manufacturer data sheet.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003csup\u003ec\u003c/sup\u003e \u003cem\u003eObtained from M.G. Chemicals product technical data sheet.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003csup\u003ed\u003c/sup\u003e \u003cem\u003eObtained from Chemtronics product technical data sheet.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Manufacturing\u003c/h2\u003e \u003cp\u003eAfter cutting the copper, brass and aluminium foils to a desired rectangular size as required for the composite test specimens, they are rinsed in acetone and dried to remove any dust particles before being applied on the carbon fibre prepreg. Manufacture of the laminates is similar to standard composite curing procedures for prepreg layups. The carbon block comprising of one, two, or four carbon plies is stacked on top of the single glass layer. A non-stick template with stencil like cut outs is used on top of the carbon block to accurately mount the electrodes at the required locations on the CFRP laminate as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. After positioning the metal foils, they are gently pressed by hand onto the prepreg layup to ensure secure placement once the non-stick template is removed, minimising variability in geometry and alignment across specimens. The use of a non-stick template ensures precise electrode placement, enhancing reproducibility in electrode integration across all manufactured CFRP plates. The conductive paint electrodes are drawn on the carbon fibre prepreg with a pen tip dispenser. The non-stick stencil guide is used to deposit sufficient electrode material onto the carbon prepreg arranged next to the metal foil electrodes as indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a). This manual painting process has less control over the exact shape and thickness of the final epoxy electrode. In addition to the copper foil electrodes, a copper tape electrode with conductive adhesive backing is also tested which was directly applied to the prepreg without rinsing in acetone. Before curing the sample a release agent is gently applied on the thicker electrodes shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a), 100 and 200 microns foil top surface to repel or discourage resin build up. The composite plate specimen with all electrodes in place are then vacuum bagged and transferred to an autoclave for curing. The plates are cured in an autoclave for 90 minutes at 125\u0026deg; C and 7 bar pressure as recommended by Hexcel in the 913 epoxy resin data sheet. After curing the CFRP plate with all the different electrodes, individual specimens with two electrodes at either side are carefully cut from the composite plate, as shown schematically with the dash-lines in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. This process is repeated for the 15 plates manufactured having 1, 2 and 4 carbon layers.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Test plan and electrodes arrangement\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eEffects of electrode material and geometrical variation on the measured longitudinal total electrical resistance is studied and factors that lead to a stable connection with low contact and interface resistance with CFRP are investigated. The longitudinal total resistance is independently measured for variation of electrodes with different (i) thickness (ii) length (iii) width offset and (iv) materials. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e schematically shows the electrode arrangements in the manufactured CFRP plates which are subsequently cut into individual specimens to examine the effect of these variables on the measured total resistance. The variation of electrodes is repeated for 1, 2 and 4 UD thin-ply carbon layers (1CL, 2CL and 4CL) with five repeats each, except for the length and width offset tests having three repeats. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarises the experimental test plan for variation of electrode parameters. The width of all the electrodes used for testing is 20 mm except in the electrodes length test, which had a width of 10 mm as stated in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental test plan to study the performance of embedded co-cured electrodes to establish a stable electrical contact with CFRP composites.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eInvestigated electrode parameters\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eElectrode materials\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eElectrodes length\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eElectrodes width\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eElectrodes thickness\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eElectrodes width offset\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eDistance between electrodes\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eNo. of carbon layers\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eSchematic representation\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eL (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:b\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eT (\u0026micro;m)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eO (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e(CL)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThickness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCopper, brass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10, 20, 30, 40\u003csup\u003ea\u003c/sup\u003e, 50, 80\u003csup\u003ea\u003c/sup\u003e, 100, 200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1, 2, 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a)\u003c/p\u003e \u003cp\u003eand (b)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCopper\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5, 5, 10, 20, 30, 40, 50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (c)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth offset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCopper\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0, 4, 8, 12, 16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1, 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (d)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterials\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCopper, brass, aluminium\u003csup\u003eb\u003c/sup\u003e, copper tape with conductive adhesive\u003csup\u003ec\u003c/sup\u003e, nickel paint\u003csup\u003ed\u003c/sup\u003e and silver paint\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10, 20, 30, 40\u003csup\u003ea\u003c/sup\u003e, 50, 80\u003csup\u003ea\u003c/sup\u003e, 100, 200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1, 2, 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ea\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eOnly for copper (Cu).\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003eb\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eAluminium (Al) thickness is 12 \u0026micro;m.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ec\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eCopper tape with conductive adhesive has a total thickness of 85 \u0026micro;m.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ed\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eThickness of nickel (Ni) paint and silver (Ag) paint was not controlled due to their paint nature.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSchematics in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) show the arrangement of electrodes with different thickness and electrode materials used in this study. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (b) provides side view of the individual specimen after it has been cut from the composite plate. To investigate the effect of electrode length on the total measured resistance, a separate composite plate is manufactured, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (c), with individual specimens cut out for testing. In practice, electrodes might have offset or misalignment which can affect the measured experimental resistance and therefore, studying offset between electrodes edges as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (d) is also important. Tests are also conducted to investigate the influence of electrode material in contact with carbon fibres by studying the measured total resistance with different electrode materials set which include Cu, brass and Al foils as well as Ni paint and Ag paint as outlined in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In addition to these electrode materials as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a), a Cu tape with conductive adhesive backing having a total thickness of 85 \u0026micro;m (35 \u0026micro;m Cu foil\u0026thinsp;+\u0026thinsp;50 \u0026micro;m conductive adhesive) was also used, as the tape manufacturer claimed the conductive adhesive has better bonding. These electrodes set are later cut and sectioned for microscopy analysis to examine the fibre-electrode interface contacts. The micrographs are presented in section 6.4 optical microscopy results of co-cured electrodes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Resistance measurement\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eTwo-point probe (2-pp) method using a standard handheld digital ohmmeter with an accuracy of \u0026plusmn;\u0026thinsp;0.5\u0026ndash;0.8% is used to measure the experimental total resistance. Results obtained from this was previously compared with resistance readings obtained using a NI-DAQ unit and the values were found to be within 0.5-1%. Devices like Kelvin clips are not required for use in this study. A four-point probe (4-pp) method which eliminates the contact resistance in its measurements is typically useful for measuring very low resistance values or in high contact resistance cases. However, the objective of this paper is not to characterise the electrical resistance of the CFRP layer but to study the performance of the embedded co-cured electrodes in providing a low contact resistance interface for the measuring probes. Therefore, the contact resistance needs to be included in the experimental measurements to assess if this technique can provide a stable low contact resistance connection.\u003c/p\u003e \u003cp\u003eOne common approach to measure the contact resistance and its constituents i.e. interface and spread resistance is to use two-point probes on several samples with varying distances between the electrodes to obtain results similar to our FE results in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. However, implementing this experimentally for the entire range of materials and configurations of interest would require significantly large number of tests. To address this, FE analysis as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e is used to estimate the spread based on varying distances between the electrodes and for the experiments, the distance between the electrodes is kept constant and the obtained values are compared against each other as well as the FE and the analytical results. This combined approach provides reliable insights into contact resistance between electrodes and carbon fibre in composite materials. All the tests conducted in this research measured the composite specimen resistance at room temperature.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.5 Pull-off measurements to assess mechanical bonding of the co-cured electrodes\u003c/h2\u003e \u003cp\u003eThe adhesion strength between the co-cured electrodes and the CFRP layers is measured using a portable adhesion testing unit, P.A.T handy (DFD\u0026reg; Instruments), in accordance with a modified version of ASTM-D4541-17. Steel stubs with 2.8 mm radius are adhesively bonded to the electrodes using DFD\u0026reg; E1100S epoxy, which is cured for 60 min at 140\u0026deg;C, and then left to cool to room temperature. Electrodes are cleaned with compressed air, and air bubbles formed between the stub and electrode are carefully removed through pressing of the stubs. Any excess epoxy following curing is removed via a cylindrical cutting tool supplied with the equipment. Load is applied hydraulically through 4 pins surrounding the stub, applying force against a ring between the electrode and tester, enabling even force distribution. Each of the stubs are then pulled-out vertically with a calibrated hydraulic pump until detachment. The adhesion strength is determined from the recorded failure value divided by the quantified detached surface area. Analysis of the failure sites was conducted using a JEOL 6490LV scanning electron microscope. For adhesion measurements, a modified standardised set up was employed due to the nature of the samples being tested. A stainless-steel plate was attached behind the CFRP to provide stability due to its flexibility.\u003c/p\u003e \u003c/div\u003e"},{"header":"6 RESULTS","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e6.1 Effect of autoclave curing\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows variations in the measured total resistance before and after curing the composite laminate with copper electrodes of different thickness. In the uncured stage, a higher total resistance is observed as the electrodes are not embedded in the composite. Instead, they are firmly pressed down by hand into the prepreg laminate and subsequently the uncured total resistance is recorded. Hence, the uncured total resistance values are susceptible to large variations, as shown by the large scatter in the error bars in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. It is evident that uncured total resistance is always significantly higher than cured total resistance and the theoretical CFRP resistance value. Therefore the contact resistance is high before the composite and electrodes are co-cured. After the laminate is cured, the electrodes are embedded in the composite to form a stable interface as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e micrograph and the cured total electrical resistance is close to the theoretical CFRP resistance found using Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This demonstrates that co-curing electrodes along with carbon fibre prepreg with external pressure can significantly reduce the contact resistance. Furthermore, the average cured total resistance of the 4 carbon layers (4CL) specimens has a low scatter demonstrating the repeatability of the resistance measurements among different samples.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Electrodes geometrical variation\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the variation of the cured total resistance with respect to the copper electrodes thickness for three different CFRP layer thickness. The average measured cured total resistance values of 1CL, 2CL and 4CL specimens displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e are all close to their respective theoretical CFRP resistance values, especially for 1CL and 2CL specimens with electrode thickness between 20 and 200 microns. This indicates that the cured total resistance is largely independent of the electrode thickness. As per Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) the contact resistance value for a single electrode is calculated from the difference between the cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, and the CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, divided by 2. In the case of 4CL samples the average contact resistance value is 0.31 Ω. This includes both interface resistance and spread resistance as highlighted in Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Section 4 explains using FE analysis to calculate the spread resistance and for a single electrode contact in 4CL it is estimated to be 0.11 Ω as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. This suggests that the average interface resistance for 4CL laminate is only 0.20 Ω. Similarly, for 1CL and 2CL laminates, the average contact resistance from the experiments is found to be 0.16 Ω and 0.14 Ω respectively. And from the subsequent FE analysis, the estimated spread resistance is 0.08 Ω (1CL) and 0.09 Ω (2CL). Therefore the average interface resistance for 1CL and 2CL equates to be 0.08 Ω and 0.05 Ω respectively. The average coefficient of variation (CV) of all 1CL, 2CL and 4CL samples are 5.1%, 3.7% and 6.7% respectively as provided in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Therefore the results are deemed repeatable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCarbon fibres exhibit slight undulations, and it is widely accepted that these undulations cause individual fibres to come into contact with each other. This contact is responsible for electrical flow in the transverse direction. Varying the electrodes length examines whether there exists a minimum electrode length necessary to achieve this contact between the fibres and the electrodes. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the effect of varying electrodes length in the fibre direction on the cured total resistance of one carbon layer specimens. Distance between the inner edges of the two copper electrodes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is kept constant and equal to 20 mm, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (c). The measured cured total resistance of the 1CL composite specimen shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e are similar for all electrode lengths from 2.5 mm to 50 mm and are close to the theoretical CFRP resistance value. This suggests that copper electrodes with lengths as short as 2.5 mm still have a low interface resistance. The error bars show only a small variation of the resistance between different samples and hence the obtained results are consistent in establishing a good contact with carbon fibres in the CFRP layer.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the cured total resistance against variation of electrodes width offset (O) in 1CL and 2CL specimens compared with their theoretical CFRP resistance calculated using Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) having overlapping width. Increasing the width offset O, increases the measured cured total resistance of the composite in both 1CL and 2CL specimens. This increase is driven by the reduction in the effective overlap width \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{overlap}\\)\u003c/span\u003e\u003c/span\u003e of the longitudinally conducting carbon fibres between the two electrodes. Therefore, it increases the overall measured longitudinal total resistance which is compatible with the analytical Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e6.3 Electrode material\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e compares the effect of the electrode materials, i.e. copper and brass, on the cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, with respect to their theoretical CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, in 1CL, 2CL and 4CL samples for varying thickness of electrodes. Only the average total resistance is shown, and the error bars are not displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e to maintain clarity. The coefficient of variation of both electrode material is shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In electrodes with similar thickness, the copper electrodes always provide lower total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, values and are closer to the theoretical CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, when compared against the brass electrodes. This response is consistent in all 1CL, 2CL and 4CL specimens. Also, the CV of results for copper electrodes are smaller than brass electrodes results as provided in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Additionally, the average total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, values for aluminium foil, Cu tape with conductive adhesive, nickel paint and silver paint are represented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. These electrode materials result in a higher total resistance and CV compared to copper electrodes.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage measured cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, values of 1, 2 and 4 carbon layers CFRP specimens with different electrode materials.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e\u003cem\u003eElectrode material\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003eCFRP specimen\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e1CL\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e2CL\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e4CL\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e6.23 Ω \u0026ndash; Ohm\u0026rsquo;s law\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e3.11 Ω \u0026ndash; Ohm\u0026rsquo;s law\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e1.56 Ω \u0026ndash; Ohm\u0026rsquo;s law\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{spread}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e0.153 Ω \u0026ndash; FE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{spread}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e0.177 Ω \u0026ndash; FE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{2\\times\\:R}_{spread}=\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e0.223 Ω \u0026ndash; FE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e (Ω) [CV%] \u003cem\u003eExperiments\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eContact resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInterface resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTotal resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e (Ω) [CV%] \u003cem\u003eExperiments\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eContact resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eInterface resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eTotal resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e (Ω) [CV%] \u003cem\u003eExperiments\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eContact resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eInterface resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e (Ω)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCopper (Cu)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.54 [5.1]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.39 [3.7]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.18 [6.7]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBrass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.05 [7.4]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.24 [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.95 [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAluminium (Al)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e143.78 [63]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e137.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e137.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e202.26 [87]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e199.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e198.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e175.64 [84]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e174.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e173.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu tape with conductive adhesive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e36.40 [44]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e17.73 [91]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e14.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e12.90 [61]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e11.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e11.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNickel (Ni) paint\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.22 [48]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.86 [46]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e8.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8.60 [55]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e7.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e6.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSilver (Ag) paint\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.00 [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.46 [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.88 [37]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e1.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eAll reported contact resistance in this table are for similar electrode surface area of 200 mm\u003c/em\u003e \u003csup\u003e \u003cem\u003e2\u003c/em\u003e \u003c/sup\u003e \u003cem\u003erectangular electrodes of 20 mm width and 10 mm length.\u003c/em\u003e\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows 1CL, 2CL and 4CL specimens cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, values of copper electrodes and brass electrodes averaged over all the thickness used in the study compared with the average, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, values of Al foil, Cu tape with conductive adhesive, Ni paint and Ag paint electrode materials. The contact resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:2\\times\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e is calculated by subtracting the theoretical CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, from the experimentally measured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, as indicated in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Contact resistance can be affected by the area of the electrode. Since all electrodes presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e have similar area, this is a representative comparison between the applied electrodes. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that copper electrodes on average provide the lowest contact resistance and the lowest CV in all carbon layer thicknesses. These values have been measured across different copper electrode thicknesses and the CV in each sample batch with similar electrode thickness would be even smaller than the values in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The measured total resistance of Ag paint electrodes has a smaller CV with a lower contact resistance when compared with Ni paint, Cu tape with conductive adhesive and Al foil electrodes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e6.4 Optical microscopy of co-cured electrodes\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the electrode/carbon fibres interface after co-curing the electrodes and the carbon fibre prepreg, which creates close contacts between them at the interface. As highlighted in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (a), the copper foil electrode is observed to have dents around the carbon fibres. This evidence suggests that the copper electrode touches the top row carbon fibres and generate a good electrical contact. Microscopy of co-cured brass electrode shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (b) indicates that they have similar electrode/carbon fibres contact with fewer interface dents compared to the copper electrodes. However, in the copper tape with conductive adhesive there is a clear gap between the electrode and carbon fibres filled with the conductive adhesive as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (c).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e (a) shows the edge of an embedded 10 microns copper electrode co-cured with two carbon layers composite specimen resulting in a smooth electrode flush at the top surface of the composite layer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e (b). It can be observed that the edge of the copper electrode is inside the composite specimen and hence has been embedded well. Similar to Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, the co-cured copper electrode is shown to have close electrode/carbon fibres contacts and dents at the interface.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the fibre orientation angle of 2.9⁰ from the CFRP surface line in a co-cured specimen embedded with a brass electrode of 20 microns thickness. UD carbon fibre prepregs are known to have fibre mis-orientation angle of \u0026plusmn;\u0026thinsp;2\u0026ndash;3 degrees and waviness along the fibre direction [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. This shows that the co-cured electrodes are not introducing a significantly larger misorientation and therefore, will not significantly compromise the mechanical properties of the composite layer.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e shows the nickel paint and silver paint electrodes at their respective electrode/carbon fibres interface. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e (a) exhibits a heterogenous texture of the nickel particles making up the electrode layer with micro pockets of polymer matrix in between. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e (b) displays silver particles forming a more homogenous electrode layer and therefore has a better contact with carbon fibres resulting in a lower contact and interface resistance. Hence the measured total resistance is closer to theoretical CFRP resistance when compared to nickel paint electrodes, as presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e6.5 Pull-off test\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn a pull-off test, predominantly three modes of failure may occur: full interfacial failure of electrode/CFRP interface, partial interfacial failure of electrode/CFRP interface, and failure of the adhesive between the stub and electrode. Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e shows typical SEM images and EDX maps of these three failure modes after test is carried out. For accurate measurement of the interfacial strength, full interfacial failure is preferred since one can ascertain the force required for failure of the bond between the electrodes and the CFRP beneath. Failure of the adhesive between the stub and electrode gives an indication that the force required to break the bond between the electrode and CFRP is in excess of the adhesive\u0026rsquo;s strength and therefore gives a lower bound to the strength of the bond between the electrodes and the carbon layer.\u003c/p\u003e \u003cp\u003eTo highlight the variance on electrode thickness, the copper electrodes with 20, 50, and 200 micron samples are tested as copper electrodes used in this paper have the lowest interface resistance. Since the standard (ASTM-D4541-17) was designed for flat, rigid, metal surfaces, a reduction in average adhesive strength, as stated within the defined standard, may be seen due to flexing/bowing of the substrate materials generating additional coating stresses thus resulting in premature failure (such as those used in this study).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePull-off adhesion data demonstrating average failure strength of co-cured copper electrodes (n\u0026thinsp;=\u0026thinsp;4). Additionally, the frequency of each failure mechanism has been detailed.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eElectrode sample\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eFailure strength (MPa)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eFull electrode/CFRP interfacial failure\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ePartial electrode/CFRP interfacial failure\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eElectrode/stub adhesive failure\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu 20 \u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.4\u0026thinsp;\u0026plusmn;\u0026thinsp;3.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu 50 \u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMore than 25.0\u0026thinsp;\u0026plusmn;\u0026thinsp;3.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu 200 \u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMore than 24.6\u0026thinsp;\u0026plusmn;\u0026thinsp;2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the obtained pull-off test results. The thickness of the electrode exhibits an effect, with the thicker electrodes exhibiting higher failure loads. Additionally, for the copper electrodes with thickness of 50 and 200 microns both exhibited purely adhesive failure at about 25 MPa as presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. This indicates that the bond strength between the electrode and the CFRP layer is higher than 25 MPa. Due to the failure of adhesive between the stub and electrode it has not allowed application of higher loads for the measurement of the precise bond strength between the electrode and the carbon layer. The 20 microns thick copper electrode samples exhibited partial failure of the electrode at about 11 MPa, indicating a lower failure strength compared to the thicker counterparts.\u003c/p\u003e \u003c/div\u003e"},{"header":"7 DISCUSSION","content":"\u003cp\u003eComparison shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e between the longitudinal CFRP resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{CFRP}\\)\u003c/span\u003e\u003c/span\u003e, and the experimentally measured cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, demonstrates that the electrode co-curing technique provides a stable, repeatable and low electrical contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e, with almost all copper electrodes especially those with a minimum thickness of 20 microns. These findings establish co-cured electrodes as a better alternative to post-cure methods, offering a simpler, more reliable solution for achieving stable electrical contact in CFRP composites without additional surface preparation or fibre damage. The FE modelling results helped estimating the spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e, in different CFRP laminates with different carbon layer thickness which is found to noticeably contribute to the contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e of the co-cured copper electrodes as described in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Hence the interface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e, is found to be low in co-cured copper electrodes suggesting that they indeed achieve a robust electrical connection in CFRP composites. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e indicates no significant effect of electrodes thickness on the cured total resistance of the CFRP laminate. Whereas from Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e it can be noted that electrodes can be as short as 2.5 mm and still provide a good electrical contact with the carbon fibres.\u003c/p\u003e \u003cp\u003eUsing a copper sintering approach a contact resistance per unit electrode area of 9.3\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e was observed [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Whereas sintering using silver nanoparticles resulted in an average contact resistance per unit electrode area of 3.66\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] and 4\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Although the electro-copper plating technique on carbon fibre composite led to a contact resistance per unit electrode area of 6.9\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], due to the complexity and hazardous nature of the process this method is not suitable for large structures. In this work, the average contact resistance per unit electrode area of the co-cured copper foil electrodes shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for 1CL, 2CL and 4CL specimens are 7.75\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, 7\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e and 1.55\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e respectively. The obtained contact resistance using the co-curing technique results in a very low interface resistance, lower or in the range of many other much more complicated electrode fabrication techniques.\u003c/p\u003e \u003cp\u003eSince the electrodes are mounted on CFRP before curing the composite, the need for any surface preparations e.g. sanding, polishing or laser treatment is eliminated. Such treatments would be typically necessary if electrodes are applied to a cured composite specimen. It is observed from the gathered experimental total resistance data, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, that the uncured total resistance measured before curing of a composite laminate is significantly higher than the theoretical CFRP resistance and also has a large scatter as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. During the autoclave curing process, as the temperature increases the thermoset resin in the prepreg changes from a gel form to a low viscosity medium. The vacuum and external pressure applied to the prepreg laminate at elevated temperature press the electrodes into the prepreg, embedding them in the CFRP laminate. It is worth mentioning that while manufacturing the samples, two of the specimens shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) went through failed curing cycles with no vacuum and external pressure, and the resulting electrodes had high contact resistance similar to the uncured total resistance shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. After a successful curing cycle, the cured total resistance measured are much lower with a low CV as described in section 6.2 and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (a), (b) and Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e (a) show the interface having a direct electrode to carbon fibres contact. A smooth flush top CFRP surface is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e (b) therefore the co-cured electrodes are well bonded to the laminate. The performed pull-off measurements presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e provide the interfacial strength of the co-cured electrodes and the failure modes are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e. In electrodes with 50 and 200 micron thickness, the electrode/CFRP bond performed better than the epoxy used to glue the stub and electrode, meaning that the bond between electrodes and CFRP laminate has a minimum of about 25 MPa strength. The 20 micron copper electrodes provided an average tensile bond strength of 11.4 MPa which shows a relatively good lower bound for the bond between the electrode and CFRP, meaning the electrodes do not de-bond from the CFRP layers easily. Pull-off test results demonstrate that co-cured electrodes maintain sufficient mechanical bonding strength with the CFRP substrate, with misalignment angles remaining below 3\u0026deg; as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. These findings confirm that the integration of embedded electrodes does not compromise the structural integrity of the composite, supporting their potential in advanced multifunctional materials.\u003c/p\u003e \u003cp\u003eUse of metal foil electrodes provides a good degree of control on electrode shape, geometrical parameters and is easy to apply on carbon fibre prepregs. Microscopic images of the electrodes show them embedded well into the composite top layer and are fixed in place after curing. Reducing the electrode thickness may have its advantages to minimise fibre misalignment and any impact on mechanical properties of the composite, however our results show that thicker electrodes exhibit higher bond strength with the CFRP layer. In this study, copper electrode with the thickness of 20 microns provided minimal interface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e, with acceptable bond strength to the composite layer.\u003c/p\u003e \u003cp\u003eThe experimental results in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e show that the copper tape with conductive adhesive backing gives higher contact resistance compared with bare surface copper electrodes. Therefore, having a conductive glue layer on the copper foil hinders the achievement of a good electrical contact between the electrodes and the CFRP laminate. Due to the paint form at the time of application, it is more difficult to control the shape and size of both nickel paint and silver paint electrodes shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e. When these paints are applied to carbon fibre prepregs before curing, particles are observed to seep through the carbon ply. Additionally, they require 20 to 30 minutes drying time to avoid surface spreading while bagging the composite laminate for autoclave processing. Hence conductive paints are less favourable electrodes and are more challenging to maintain repeatability.\u003c/p\u003e \u003cp\u003eAluminium electrodes have the highest contact resistance of all the tested materials. This is deemed to be due to oxidation of aluminium surface [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] which is electrically insulating and quickly forms around the metal and cannot be washed with acetone. From Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e it is clear that the cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, of samples with aluminium electrodes are significantly higher than that of brass electrodes, however we know that resistivity of brass is higher than resistivity of aluminium as noted in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Similarly we can see that total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, of samples with brass electrodes are higher than that of silver paint electrodes, whereas the resistivity of silver paint is much higher than that of brass. Additionally, the resistivity of copper is less than half that of aluminium, however the achieved contact resistance value using the co-cured aluminium electrodes is several magnitudes higher than co-cured copper electrodes. Furthermore, as listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e the resistivity of nickel paint is an order of magnitude higher than silver paint, this is a contributing factor in the higher contact resistance observed in nickel paint electrodes as compared in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e with the heterogenous composition of the nickel particles. These results indicate that several factors e.g. surface topography, contact pressure, material property and chemical conditions at the contacting surfaces in addition to electrode material resistivity can affect the value of interface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e, and consequently the contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e, between the CFRP and electrodes.\u003c/p\u003e \u003cp\u003eFrom the FE analysis the CFRP resistance found for 1CL, 2CL and 4CL are 5.9 Ω, 3.3 Ω and 1.6 Ω respectively. The total composite resistance for the models without the 1-micron interface between electrodes and the CFRP layers were exactly the same when the longitudinal and transverse resistivity values were applied to the 1-micron interface layer. However, the results showed a significantly higher resistance of 1E6 Ω when resin resistivity was applied. Since the experimental total resistance are much lower than such values, and quite close to the theoretical CFRP resistance, it can be noted that a good contact between carbon fibres and electrodes has been achieved experimentally. Otherwise, a slight separation of 1 micron between fibres and electrodes could lead to much higher experimental resistance measurements.\u003c/p\u003e"},{"header":"8 CONCLUSIONS","content":"\u003cp\u003eThis study systematically evaluates how key electrode parameters influence the contact resistance in CFRP composites, establishing co-curing as a practical and non-invasive technique for embedding electrical connections. This paper demonstrates a non-invasive and simple electrode manufacturing technique to establish a reliable low-contact and interface resistance electrical connection with carbon fibres in CFRP composites. Most existing methods used in establishing electrical contact are based on applying the electrodes to cured composite specimens. This typically involves surface preparation that can introduce damage to the composite and the carbon fibres. These methods can be expensive, laborious, time consuming, and complex to execute. Co-curing thin metal foil or conductive paint electrodes on CFRP facilitates direct electrode/fibres contact without any fibre damage or the need for any additional fabrication stages e.g. surface preparation or extra curing cycles. The experimental results show a small scatter in the cured total resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{Total}\\)\u003c/span\u003e\u003c/span\u003e, using copper foil electrodes with the lowest contact resistance per unit electrode area of 7\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. The spread resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{spread}\\)\u003c/span\u003e\u003c/span\u003e, obtained from FE simulation has a sizeable contribution in the total contact resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{contact}\\)\u003c/span\u003e\u003c/span\u003e, experimentally observed between the measuring copper electrodes and the CFRP. This contribution of the spread resistance infers that the influence of interface resistance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{interface}\\)\u003c/span\u003e\u003c/span\u003e, is low in the co-cured copper electrodes. This study provides an accessible, low-cost, and practical approach for integrating electrical connections into CFRP composites. These results have implications for the design of multifunctional materials in aerospace, automotive, and energy sectors, where robust electrical performance is critical.\u003c/p\u003e \u003cp\u003eSpecific findings from this study are summarised below:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eEffect of electrodes material: co-cured copper foil electrodes have the lowest contact and interface resistance, followed by silver paint, brass foil, nickel paint and Cu tape with conductive adhesive. Silver paint forms a relatively homogenous continuous electrode layer and has a lower contact resistance than nickel paint electrodes. Aluminium electrodes have the highest contact resistance.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eElectrodes thickness: the thickness variation in copper foil electrodes from 20 microns upwards does not affect the measured cured total resistance and has consistently low contact and interface resistance values. A slightly higher contact resistance was observed for the foils with a thickness of 10 microns.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eElectrodes length: a variation of copper electrodes length greater than 2.5 mm has no tangible effect on the interface resistance.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eElectrodes width offset: increasing the width offset between the two electrodes decreases the total effective width (overlap width), thereby increasing the measured total resistance. The change in the resistance follows Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) up to an offset close to the electrode's width.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCuring cycle: the measured uncured total resistance is significantly higher than the cured and theoretical CFRP resistance. The CFRP curing cycle requires an active vacuum and external pressure to achieve a uniform electrode and carbon fibre interface with low contact resistance.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS.A.M. (Sheik Abdul Malik) conducted the manufacturing, experimental work, validation, methodology, investigation, formal analysis, and conceptualisation. S.A.M. also prepared the original draft of the manuscript.M.J. (Meisam J.) provided guidance on the experimental design, contributed to the investigation, formal analysis, and conceptualisation, and reviewed and edited the manuscript.M.D.W. (Matthew D. W.) performed the pull-off tests and analysis and contributed to writing and editing.J.D.A. (Jose D. A.) conducted the FE simulations and contributed to writing and editing.R.M.F. (Reda M. F.) assisted with review and editing.All authors reviewed and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eSheik Abdul Malik expresses heartfelt gratitude to Miss Maisie Keogh for her invaluable support during this research work. He also extends sincere thanks to his parents, Abdul Salam and Fathima Zohara, for their unwavering sacrifices, which made this research endeavour possible. The authors acknowledge Hexcel for supplying glass prepreg layers for this research. All data required for reproducibility are provided within the paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eTodoroki, A., Yoshida, J.: Electrical resistance change of unidirectional CFRP due to applied load. JSME Int. J. Ser. Solid Mech. Mater. Eng. \u003cb\u003e47\u003c/b\u003e(3), 357\u0026ndash;364 (2004). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1299/jsmea.47.357\u003c/span\u003e\u003cspan address=\"10.1299/jsmea.47.357\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbry, J.C., Choi, Y.K., Chateauminois, A., Dalloz, B., Giraud, G., Salvia, M.: In-situ monitoring of damage in CFRP laminates by means of AC and DC measurements. Compos. Sci. 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Conf. no. \u003cb\u003e1\u003c/b\u003e, 442\u0026ndash;447 (2005). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/IAS.2005.1518345\u003c/span\u003e\u003cspan address=\"10.1109/IAS.2005.1518345\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-composite-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"acma","sideBox":"Learn more about [Applied Composite Materials](http://link.springer.com/journal/10443)","snPcode":"10443","submissionUrl":"https://submission.nature.com/new-submission/10443/3","title":"Applied Composite Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Contact Resistance, Electrical properties, Longitudinal Resistance, Co-Cured Electrodes","lastPublishedDoi":"10.21203/rs.3.rs-5639196/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5639196/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAchieving robust low-resistance electrical contact with carbon fibres embedded in polymeric matrices is a challenge and different electrode fabrication methods, mostly for after composites are cured have been examined in the literature. This paper investigates the use of metallic foils co-cured on the top surface of carbon fibre reinforced polymer (CFRP) composites to form stable electrodes. Different electrode materials and the effects of their geometry variation on the CFRP to electrode interface resistance (IR) are studied experimentally. Finite element (FE) analysis is used to estimate the spread resistance (SR), providing a reliable estimation of the interface resistance between different electrodes and CFRP specimens. Copper is found to be the optimal electrode material and has a low interface resistance per unit electrode area ranging from 2.75\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e to 1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Ωmm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e independent of geometry parameters. The mechanical bonding between the electrodes and the composite has been examined using pull-off tests and the obtained results show that the electrodes have an acceptable mechanical bonding with the composite layer. In comparison to other electrode fabrication processes, the co-curing technique is significantly easier, less invasive and more cost-effective as it eliminates the need for altering or introducing surface damage to CFRP specimens.\u003c/p\u003e","manuscriptTitle":"Robust Electrical Contact With Low Interface Resistance Using Embedded Co-cured Electrodes in Carbon Fibre Composites","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-17 14:16:29","doi":"10.21203/rs.3.rs-5639196/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-02-12T12:23:38+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-02-04T02:07:38+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-19T14:09:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"284362494866044067406749098915370656052","date":"2025-01-19T13:54:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"301711400896201776978463341230095248915","date":"2025-01-16T04:39:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"284448295066832106771662618826219860466","date":"2025-01-15T22:51:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"83085232244578097769129617924632002477","date":"2025-01-06T09:18:57+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-12-22T16:54:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-12-16T03:33:57+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-12-16T03:32:17+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Composite Materials","date":"2024-12-13T15:15:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-composite-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"acma","sideBox":"Learn more about [Applied Composite Materials](http://link.springer.com/journal/10443)","snPcode":"10443","submissionUrl":"https://submission.nature.com/new-submission/10443/3","title":"Applied Composite Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"67f0557f-626a-49ca-b812-69db6be3cf94","owner":[],"postedDate":"January 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-06-23T15:59:09+00:00","versionOfRecord":{"articleIdentity":"rs-5639196","link":"https://doi.org/10.1007/s10443-025-10345-1","journal":{"identity":"applied-composite-materials","isVorOnly":false,"title":"Applied Composite Materials"},"publishedOn":"2025-06-19 15:57:09","publishedOnDateReadable":"June 19th, 2025"},"versionCreatedAt":"2025-01-17 14:16:29","video":"","vorDoi":"10.1007/s10443-025-10345-1","vorDoiUrl":"https://doi.org/10.1007/s10443-025-10345-1","workflowStages":[]},"version":"v1","identity":"rs-5639196","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5639196","identity":"rs-5639196","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}