Carbon fibres ,Electrical properties ,Anisotropy , 00-01,99-00 INTRODUCTION Carbon fiber reinforced polymers (CFRP) offer great advantages over conventional materials, mainly due to their high specific strength and stiffness. However, lightning strikes pose a serious natural threat to high rise structures, such as wind turbines, as well as airplanes made of, or containing significant amount of composite materials . Modeling the lightning current interaction with CFRP is a challenging problem . Good understanding of the CFRP material properties is the key to precise numerical models . The electric conductivity has significant influence on current distribution and also on power densities. As an anisotropic material, CFRP has higher conductivity along the fiber direction, but much lower conductivity in the depth and transverse directions , which makes the electrical current tending to concentrate on the surface near the lightning attachment point. A simple constant conductivity assumption might lead to extremely high Joule heat and unrealistic temperature . Although the conductivity is assumed to depend on temperature in many models , it is seldom considered to be relevant to electric field. While several experiments have been performed for electric conductivity under low current and room temperature, the number of investigations dealing with non-linear characteristics of CFRPs is limited . Chekanov et al. has observed the breakdown effect of CFRPs with short cut fibers, which have much lower fiber content and also electric conductivity. Sun et al. compared the dynamic impedance of several CFRP specimens with emphasis on material surfaces. The depth direction conductivity of long fiber reinforced polymers might exhibit non-linearity under high voltage as well, owing to the sandwiched polymer between plies, which requires more detailed investigation. The objective of this paper is to experimentally study the non-linear current-voltage behavior of CFRP samples along the depth direction. The rest of the paper is organized as follows. Section 2 discusses the method and the test fixture. The obtained data are presented and discussed in Section 3. Conclusions are given in Section 4. EXPERIMENTAL Low resistivity, high current, high voltage and drastic heat dissipation pose challenges to the measurement of the non-linear electric conductivity of CFRPs. The first three points were taken into consideration in the test fixture, while the last was mitigated by using an impulse source. Moreover, small specimens were used to increase the resistance along the depth direction. Samples CFRP plates with plies [ ± 45∘/0∘/45∘/0₂∘/90∘/−45∘/0∘]S were made from MT300 carbon fibers and 603 polymer. After being produced with autoclave process, the plates were cut by a milling machine to get round specimens with a diameter and thickness of 11 mm and 2.7 mm, respectively. All the specimens have resistances along the depth direction from 30 to 50 Ω, which means the conductivity ranges from 0.688 to 1.15 S/m in this direction. Test fixture Although carbon fibers are not as conductive as metals, they are still good conductors. After breakdown, the resistance of specimens might drop to a low value, even below 1 Ω. Therefore, the 4-probe method is required to precisely measure the resistance which, otherwise could be easily overwhelmed by the resistance of contacts and wires. A robust connection between the electrode and the specimen is also necessary to sustain the high current. Conductive paste was tried as contacts between electrodes and specimens during preliminary experiments. However, it failed just after the inception of a breakdown. Moreover, CFRPs are anisotropic materials. The conductivity in the fiber direction is much larger than that in the depth direction, which makes the voltage between the upper and bottom edges almost the same as the driving electrodes, even if the specimen has a diameter several times lager than the electrode dimension. As a result, air breakdowns sometimes happen prior to specimen breakdown. Therefore, a specifically designed fixture was fabricated to overcome these challenges, as described in what follows. The profile and photo of the fixture are shown in Fig. [fig:testFixture] and Fig. [fig:fixtureSpecimen], respectively. The specimen is clamped between the 2 brass tubes, which form the 2 driving probes. Inside each tube, there is a brass pin isolated by PA6 nylon, which is the sensing probe. The brass tube, the nylon insulator, and the brass pin, form a coaxial structure. Because the conductivity along the fiber direction is several tens of times larger than that along the depth direction, the current can be distributed quite uniformly on the contacting ply before going deep into the specimen. The 2 coaxial structures are mounted with screw on 2 stainless steel plates respectively. The top and bottom halves are insulated by 3 black polyformaldehyde plastic pillars. The screws exist on the inner surface of the plates, inner and outer surface of the tubes and nylon isolators, and also the outer surface of the pins. By turning the tubes while fixing the plates, pressure could be applied to the specimen in order to robustly attach the driving probes to the specimens. Before impulse testing, the specimens were inserted into the fixture to measure the DC resistance. Tightening torques of 1 Nm and 1.5 Nm were applied to the brass tubes successively, with less than 1% differences of resistance observed, which implies that 1.5 Nm is sufficient for achieving a good contact. By rotating the insulators with respect to the tubes, and the pins with respect to the insulators, gaps between the insulators, pins and the specimen could also be minimized. The whole fixture was immersed in rapeseed oil to prevent surface discharges on side walls of specimens. To verify this configuration, one of the specimens was further wrapped with ethylene-vinyl acetate copolymer (EVA) which has higher dielectric strength as shown in Fig. [fig:specimenEVA], but no significant difference in results was observed. Impulse source The power dissipation in CFRP would heat the specimen drastically, which makes it almost impossible to measure the non-linear characteristic with constant current. Therefore, pulses were injected to prevent drastic temperature increments and polymer decompositions of the whole specimen. The impulse sources are listed in Table [tbl:pulseGenerators]. A 3CTEST LSS160SS source was used to generate the lightning waveform 1 of aircraft lightning standard SAE ARP 5412 , while a Montena EMP80K-5-500 source was used to generate conductive high altitude electromagnetic pulses (HEMP) conforming to the standard MIL-STD-188-125-2 . Pulses were directly injected into the 2 driving electrodes (the brass tubes) of the specimens, with their currents monitored by a BCP-619 probe. Voltages were measured from the 2 measuring electrodes (brass pins) with a 100 MHz 6 kV high voltage differential probe. To mitigate electromagnetic interference, the cables of the voltage measurement probe were arranged as close as possible and screened as shown in Fig. [fig:cableShielding]. RESULT During the test, the short-circuit current setting of the pulse source was increased by 3 dB per test step, that is, $\sqrt2$ times of the previous step. (Due to the finite source resistance shown in Table 1, the monitored actual current increment per step was a little larger than 3 dB.) Each specimen only experienced 1 test cycle. After the current was increased step by step to the maximum and then decreased back to the initial value, the specimen was replaced to avoid severe cumulative damages. Surface damages have never been observed during the whole experiment. The current and voltage waveforms of a specimen with an injected 6.4/69 μs pulse are shown in Fig. [fig:waveformLemp] (short-circuit output set to 800A). The current waveforms were still in good double exponential shapes, while some voltage distortion could be observed in the first few microseconds. The plot of the peak voltage versus peak current is shown in Fig. [fig:viLemp]. The V-I curve is not a straight line, which shows the non-linear effect. The voltage increment significantly slows down after about 470 V. The arrows in the figure represent the sequence of test steps. The DC resistance was measured again after each pulse, as shown in the same figure. Compared to its initial value, the resistance drops significantly after breakdown. In a lightning strike, the current is almost fixed due to the high impedance of the plasma channel . The decrement of the resistance means much less energy (several tens of times) is injected into the material after breakdown. Hence, the resistivity should not be regarded as constant in simulations. For the HEMP 20/500 ns pulse, the waveform with a peak current of 660 A is shown in Fig.[fig:waveformHemp]. The voltage waveform is characterized by a significant number of spikes in its leading edge, while the late time follows an exponential shape. To quantitatively evaluate the voltage-current (V-I) relationship, voltage values were extracted from the peak of exponential fittings of the voltage waveforms, neglecting the voltage spikes. In Fig. [fig:viHemp] shows the peak voltage versus peak current, where a non-linear behavior can be observed as well. The arrows in the figure represent the sequence of test steps. The HEMP pulse is so short that its pulse width is only 0.7 % of the 69 ns lightning WF1. Although the time duration varies by more than two decades, the turning point of the voltage is in the same order of magnitude. This implies that breakdowns relate weakly to the injected energy but more to the applied voltage or electric field. The dissipated energy within the specimen, integrated from Fig.[fig:waveformHemp] by the Joule heating formula was found to be 0.4 J, which is even not enough for the temperature of the specimen to increase on average by more than 2 K. Although the temperature rise is not uniform, drastic inhomogeneity might not appear before breakdown, leading to a local high temperature. Hence, it could be inferred that the electric breakdown mechanism rather than the thermal breakdown mechanism dominates. The electric breakdown is a fast process. Significant voltage spikes exist in the leading edge, as shown in Fig.[fig:waveformHemp]. The spikes could not be measured precisely, since they were so narrow that they had exceeded the 100 MHz probe bandwidth. Moreover, the over-range audible alert of the probe sounded during the experiment, which meant that the actual voltage spike may even approach 6 kV (the upper limit of the probe). Compared to the small voltage spikes in the waveform with low current (Fig. [fig:waveformHempLow]), these spikes should not be subjected to electromagnetic interference, because electromagnetic coupling is linear, which could not change the shape of voltage curves. The transient resistance (the ratio of voltage to current at every time point) remains almost constant after the spike (Fig. [fig:resistance]). Therefore, it seems that conductive channels form just within the spikes, within no more than a few nanoseconds. After that, the channels would provide good conductivity. The resistance measured from the waveform is slightly lower than that measured with DC after the pulse, which might be attributed to the high temperature of the channel during the pulse. Fig. [fig:waveformLemp], no spike was observed, for the rising edge of the lightning pulse was too slow. Breakdowns happened continually during the rising edge, which formed the flat tops of voltage waveforms. The above-mentioned characteristics look similar to the breakdown of thin polymer films . The formation of breakdown channels is within a short period of nanoseconds. These channels would keep their conductivity during the rest of the pulse. They are also irrecoverable, and they therefore still exist after the pulse. The breakdown field strength tends to grow slightly as the voltage rise rate increases. If the thin polymer film breakdown theory could be applied to the breakdown of CFRP, the process would be described as below. Upon applying the voltage, the electric field between the plies drives electrons into the polymer. Tunneling takes place where the electric field strength is in excess of its average value, especially where the fibers are closer between plies. The electrons are captured by traps and form space charges. As the space charges propagate toward anode, the electric field near the ply with higher potential will increase. Current amplification initiating local destruction of polymer is a consequence of space charge evolution. The intense current surge causing a breakdown channel between plies is the last stage of the electric field induced destruction of a polymer . The breakdown channels are about 10 μm in diameters. It is believed that destruction of a polymer (the formation of a hollow channel with conducting walls as a result of polymer evaporation and the formation of soot) is the outcome of Joule heat liberation and heating of the material to high temperatures by an intense surge in the current . As the inter-ply polymers are broken down layer by layer, the voltage leading edge might comprise several narrow spikes. CONCLUSION The CFRP resistivity along the depth direction is measured with the 4-probe method using lightning and HEMP impulse generators. Non-linear effects were observed. Breakdown could be caused not only by 6.4/69 us lightning pulses, but also by 20/500 ns HEMP pulses at a slightly higher voltage with much less pulse width and energy, which implies that the breakdown at these pulse widths should be dominated by the electric breakdown mechanism. By analyzing the waveform under HEMP, the electric breakdown is fast. Voltage spikes occur in the leading edge during the first few nanoseconds. The transient resistance (the ratio of voltage to current at every time point) remains almost constant after the spikes. These characteristics are similar to the breakdown of thin polymer films. All the measurements were performed with currents about 2 orders of magnitude below lightning standards and the experiments were not intended to be destructive. Although information might be acquired for understanding the onset of the lightning interaction with CFRPs, attention should be paid while analyzing the period after high current and energy are injected. Gas from decomposed resin and plasma pressure might also influence the resistance between plies. Moreover, the conductivity of CFRPs along the depth direction can significantly vary due to different ingredients and manufacturing processes. Therefore, more measurements are still needed to draw definite conclusions. If the conclusions are verified by further investigations, the relationship between the conductivity along the depth direction and the electric field should be taken into consideration, while modeling the interaction of CFRPs with lightning. Numerical models could be used in subsequent studies to better understand the involved mechanisms. REFERENCES [The profile of the test fixture] [The fixture with a specimen] [The specimen wrapped with EVA] [The arrangement and shielding of cables] [Typical voltage and current waveforms under 6.4/69 μs lightning pulse] [Peak voltage vs. peak current under 6.4/69 μs pulses] [Typical voltage and current waveforms under 20/500 ns HEMP (660 A peak)] [Peak voltage vs. peak current under 20/500 ns pulses] [Voltage and current waveforms under 20/500 ns HEMP (9.35 A peak)] [The transient resistance of the CFRP sample (660 A peak)] llllll & Waveform standard & Rise time & Pulse width & Generator & Source resistance 1 & SAE-ARP-5412 Waveform 1 & 6.4 us & 69us & 3CTEST LSS160SS & 1Ω 2 & MIL-STD-188-125-2 & 20 ns & 500ns & -------------- Montena EMP80K-5-500 -------------- : Characteristics of impulse generators & 60Ω & & & & &