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 \([\pm 45^{\circ}/0^{\circ}/45^{\circ}/0_{2}^{\circ}/90^{\circ}/-45^{\circ}/0^{\circ}]_{S}\) 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 \(\Omega\), 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 \(\Omega\). Therefore, the 4-probe method \cite{yamane2016electric} 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. \ref{fig:testFixture} and Fig. \ref{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 order of magnitude 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. \ref{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, pulse sources were incorporated to prevent drastic temperature increments and polymer decompositions of the whole specimen.
The impulse sources are listed in Table \ref{tbl:pulseGenerators}. A 3CTEST LSS160SS source was used to generate the lightning waveform 1 of aircraft lightning standard SAE ARP 5412 \cite{SAEARP5412}, 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 \cite{MILSTD188125}. Pulses were directly applied on 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. \ref{fig:cableShielding}.