Measurement and Study of Electromagnetic Emission Generated by Tensile Fracture of Polymers and Carbon Fibres

To study the EME generated by tensile fracture of polymers four different polymers were chosen to be tested. The selection comprises the thermoplastic polymers PTFE, PEEK and PP as well as a thermoset polymer of cured RTM6. These polymers were selected to represent four different elastic properties to analyse the influence of the material properties on their EME.

The mechanical properties of the thermoplastic polymers were measured according to DIN EN ISO 527-1 [36], using dog-bone specimen in tensile loading (specimen shape and dimensions in accordance to DIN EN ISO 527-2 [37]). For the testing of the properties of the brittle RTM6 slightly modified dog-bone shaped specimens were used. An ARAMIS 12M digital image correlation system was used to measure the specimen deformation. Conditioning and testing was done at standard climate conditions (23 \(^{\circ }\)C and 50% of relative humidity).

The densities were obtained using a helium pycnometer. The acquired results, as summarized in Table 1, are in accordance to those reported in literature.

The electric properties of the materials were obtained from measurements using a frequency response analyzer (frequency range: 1 Hz–10 MHz), an auto-balance bridge (frequency range from 20 Hz to 2 MHz), and an impedance/material analyzer (1 MHz–3 GHz). Figure 3 shows the measured values for the relative permittivity and the electric conductivity of RTM6, PP and PEEK. No measurements were performed for PTFE, since the literature values reported already indicate the highly insulating properties of the material [38]. In the context of our work, the conductivity is therefore assumed to be negligible. Due to the intrinsic dependency of the electric properties on frequency, we conducted measurements spanning the frequency range of interest for our experiments (0.1 kHz–1 MHz). While the measured values for the relative permittivity shows no significant variations in this frequency range, the values for the electric conductivity vary over a range of up to four orders in magnitude. Still, these materials can be considered low conducting for all of these frequencies.

For the detection of EME during failure of carbon fibres tensile tests on single fibres and thin fibre bundles of less than 50 fibres were conducted. As for the polymers, different types of carbon fibres with different cross sections and material properties were used to study the influences on the EME signals. Three types of carbon fibres from different classes, a high tenacity (HT) type, a high modulus (HM) type and a intermediate modulus (IM) type, were chosen.

Single fibre tensile tests on \(\ge \)20 single fibres each were carried out to obtain the modulus and the tensile strength of the fibres types. Fibre fixation and load application was done via mechanical clamps with cushioned clamping surfaces. A displacement rate of 10 mm/min was applied, with a free fibre length of 60 mm for the modulus determination and 10 mm for the tensile strength determination. The obtained data is summarized in Table 2.

To induce tensile fracture of the material mode I loading of tapered double cantilever beam (TDCB) specimens was chosen. The RTM6 specimens were cured in correspondingly shaped casting molds (curing process described in detail in [18]), while the thermoplastic polymer specimens were cut from plates of 5.0–5.3 mm thickness. Pinholes, notches and side-grooves were added, the latter by using a flat end mill tilted by 45\(^{\circ }\). Figure 4b shows the specific geometry and dimensions of the specimens. Our tapered design allows for self inhibiting crack growth for the more brittle materials while preventing excessive plastic deformations at the pinholes for the more ductile materials investigated. This design also offers sufficient space for the attachment of sensors. Figure 4a shows the positions of the EME and AE sensors. For the detection of the AE signals, two acoustic, KRNBB-PC point contact sensors were attached symmetrically on both, upper and lower, halves of the specimens.

The emitted electric field is expected to show a polar character, oriented normal to the crack surfaces. Thus, the orientation of the EME sensors has to be chosen accordingly. Therefore, for the detection of the emitted directional electric fields, two wires were placed around the specimens, one wire above and one below the notch, thus effectively forming a type of capacitor with “plate” normals directed along the z-axis. A trigger based acquisition was applied for all channels. The acoustic signals, detected by the AE sensors, were amplified by 20 dB using a 2/4/6 pre-amplifier without internal bandpass filter. A 40 dB\(_{AE}\) threshold, 100/1000/300 \(\upmu \)s as PDT/HDT/HLT and a sampling rate of 10 MS/s were set. An additional 20 kHz high pass filter was used for the measurement of the AE signals emitted during fracture of PP and PEEK. This removes part of the information content of the AE signals of these two polymers but was necessary to avoid overloading the AE amplifier.

The voltage signals at the EME sensor were amplified using a modification of the set-up as described in Sect. 3.1 (0 dB set-up for PEEK/ PP and 20 dB for RTM6/ PTFE). Here, the acquisition parameters were 500/1000/300 \(\upmu \)s as PDT/HDT/HLT and the sampling rate was set to 5 MS/s. The thresholds were set between 42 dB\(_{AE}\) and 45 dB\(_{AE}\) (due to minor variations in noise floor amplitudes over the course of the experiments). The term dB\(_{AE}\) denotes an amplification with respect to \(1\upmu \)V and will also be used for the EME detection throughout this text.

A tensile force was applied to the specimens using a test fixture as depicted in Fig. 4a and an universal testing machine (Zwick ZT 5.0). A 5 kN Xforce HP load cell was used to measure the load while it was applied displacement controlled by the testing machine. Different velocities for the displacement were chosen for different materials. This was necessary due to their different elasto-plastic behaviour. While the brittle RTM6 required a slower testing velocity of 1 mm/min to not initiate unstable crack propagation, the more ductile PP and PTFE required a higher testing velocity of 5 mm/min to initiate fracture in the first place instead of only showing plastic deformation at the notch and ductile failure of the material. For PEEK, fracture behaviour was the same for all of these velocities, so a testing velocity of 5 mm/min was applied.

Figure 5 shows representative load–displacement curves for each polymer type. The graph for RTM6 shows the expected piecewise crack propagation, with the result of multiple emission signals per specimen, i.e. one per macroscopic crack propagation event. Although exhibiting strong plastic deformation, each PTFE specimen also provided at least two measurable AE and EME signal pairs. PP and PEEK always failed in one, unstable fracture event, only providing one strong signal per acquisition channel. Here, PP additionally showed large plastic deformation before the final failure occurred.

The experimental set-up to measure EME generated by tensile fracture of carbon fibres is shown in Fig. 6. One end of a single fibre or a fibre bundle is fixed at the end of a flattened PEEK rod of 5 mm diameter using a two component epoxy adhesive. This way, the fibre is located directly at the centre of the rod diameter. The other end of the fibre is fixated at a PMMA slide, also using a drop of epoxy adhesive. The rod is connected to the testing machine (ZWICK ZT 5.0) and applies the load to the fibres. The load is applied displacement controlled with a velocity of 0.1 mm/min, and measured by a KAP-TC 5N load cell. The acoustic sensor is a KRNBB-PC point contact sensor located directly beneath the fibre at the bottom surface of the PMMA slide. This AE sensor placement provides the least possible influence of the propagation path, since the sensor cannot be connected directly to the fibre and has to be placed somewhere on the test fixture. The EME signals are detected by a thin copper wire near the fibres. The distance between fibres and EME sensor has to be as small as possible and was set to 1 mm. The acoustic signals were amplified by 40 dB by a 2/4/6 pre-amplifier without internal bandpass filter, while the voltage signals at the EME sensor are amplified by the two-staged amplification set-up discussed in Sect. 3.1. The thresholds were set to 40 dB\(_{AE}\) for the AE sensor and the EME sensor. Signals were recorded in synchronized mode, i.e. if a threshold is exceeded on one of the channels, signals on all channels are recorded simultaneously.

The fracture of the PEEK specimens generates the most reproducible and strongest EME signals of the four tested polymers (see Fig. 7). The load–displacement curves for the PEEK tests (Fig. 5) indicate no significant plastic deformation before brittle fracture occurs. The fracture process seems to occur in two stages. The EME signals of the first stage exhibit lower amplitudes and slower rises when compared to the second stage and the polarities of the signals show a random character. The second stage generates a fast rise to a high EME amplitude. Surprisingly, of all detected EME signals (for all polymers) only the signals generated by this second stage of the PEEK fracture are all generated with the same polarity. No specific reason for this behaviour was found (although, assuming a random polarisation, there is also a small chance to get only one polarisation direction when testing a limited number of specimens). Figure 10 shows a microscopy image of the fracture surface of an exemplary PEEK specimen, taken after the fracture tests. Here, like for the EME signals, the two stages of crack propagation are observable by means of fractographic investigation. The first part of the crack surface is fissured and rugged. Then, the surface becomes less rough and is almost completely smooth for the rest of the crack propagation. We consequently attribute the two stages observable in the EME signals to these two different fracture processes the fracture surface indicates. The crack lengths of the two stages are approximately the same while the first stage exhibits a larger crack surface area due to the rough surface. Nevertheless, the first stage generates a weaker EME signal. This could be due to different source-sensor orientations or partial compensation of differently charged surface fragments. Or, if the fracture process differs for both stages, so could the electrification process.

The fracture of the PP specimens is preceded by large plastic deformation, as can be seen in the load–displacement curves (Fig. 5) and in the microscopy image of the fracture surface (Fig. 11). The crack starts at the notch and slowly propagates through the plastically deformed zone. Crazing processes are expected during this stage of ductile fracture. This results in a rough fracture surface that appears as white in Fig. 11. No EME or AE was recorded during this part of the crack propagation so all arising AE and EME signals are below our acquisition threshold and therefore within or below the level of the noise floor. At a certain point brittle fracture starts and complete failure of the specimen occurs. The fracture surface of this failure becomes smooth after a short and rough transition zone. The total crack length of this event is indicated as length L in Fig. 11. Strong EME and AE signals are recorded for this brittle fracture process. The EME signals are slightly weaker than the ones recorded for PEEK but this may be due to the slightly shorter crack lengths or the higher distance between the sensing wires (as a result of the plastic deformation at the beginning of crack propagation). The polarisation of the EME signals appears to be random. Nevertheless, in terms of signal strength and signal characteristic the EME signals generated by fracture of PP exhibit very good reproducibility.

The fracture of the PTFE specimens was accompanied by large plastic deformation. After the initial plastic deformation, sudden fast crack growth occurs in a more brittle fashion and with measurable AE and EME. As intended by the design of the TDCB specimen geometry, and in contrast to PP and PEEK, the crack stops for the first time after a certain crack length L\(_{1}\). This length in shown in Fig. 12 and is flanked by two zones of plastic deformation and ductile fracture (white in Fig. 12). After another period of plastic deformation a second fast and brittle crack propagation phase occurs (L\(_2\) in Fig. 12) with another pair of AE and EME signals. Although the EME signals generated by the second or third macroscopic fracture event tend to have smaller amplitudes, and given some random influences on the amplitudes (like slightly asymmetric fracture and therefore slightly different source-sensor distances), we did not test enough samples to verify a direct crack length to amplitude correlation. No preferred polarisation direction was observable. Compared to PEEK and PP, the amplitudes of the EME signals emitted by the fracture of the PTFE specimens are at least one order of magnitude smaller.

For the epoxy resin RTM6 only brittle fracture is observed, starting directly at the notch tip. As for PTFE, the crack stops after a certain crack length L\(_1\) (see Fig. 13). The length L\(_1\) of this first fracture event is almost the full available specimen length. This first fracture emits a pair of well measurable AE and EME signals. Subsequently one or more additional macroscopic fracture events occur with much smaller crack lengths. The EME signals emitted by these events are very weak but still measurable with our set-up. The EME signals of RTM6 are the weakest of all tested polymers. The polarisation of the first rise in EME voltage signal seems to be completely random.

An evaluation of the acquired EME signal’s amplitudes based solely on the mechanical and electrical properties of the polymers appears to not be practicable since the polymers also exhibit different kinds of fracture mechanisms. Other influences may be the inter- and intramolecular bonding or the chemical composition in general. In any case, additional investigation is needed.

For the determination of the crack velocities we assume the voltage signals at the EME sensors to rise as long as the crack surface increases (and bonds are breaking) i.e. as long as the crack propagates. Electric relaxation is neglected since it’s time constants are much larger than the actual fracture times. As mentioned above, the signals are superpositions of electric signals generated by various sources. For the first signal rise we assume little influence by sensor and specimen movement. The higher frequencies attributed to crack wall vibration are assumed to be influenced by crack wall movement perpendicular to the crack propagation direction. We assume the low frequency part of the signal, considered to be generated by charge separation, to be a more reliable source for information about the crack’s propagation characteristic. Therefore, for the determination of the crack velocities we applied low pass filtering to all EME signals to remove the higher frequencies generated by vibrations. The filter frequency has to be low enough to filter all frequencies higher than the base signal but has to be high enough for the filtered signal to still adequately represent the base signal’s rise characteristics. For RTM6 and PTFE a 5 kHz low pass filter (butterworth, 6th order) proved adequate (see Fig. 14, top), while for the steeper rises of the PP and PEEK signals a higher cutoff frequency was needed (12 and 15 kHz, respectively, butterworth, 6th order). Furthermore, the EME signals emitted during fracture of PEEK and PP were recorded with a different set-up. For comparable results, i.e. for matching the transfer functions of both used set-ups, an additional 1 kHz high pass filter (butterworth, 1st order) was applied to all PEEK and PP EME signals. Figure 2 shows the transfer function of the PEEK/PP set-up with the applied high pass filter (light blue dots) which now matches the bandpass characteristics of the PTFE/RTM6 set-up. The additional filter only marginally influences the characteristic of the first rise of the PEEK and PP EME signals.

To determine the actual velocity profiles we use a method as is illustrated in Fig. 14. After filtering we obtain the component of the EME signals which are attributed to pure charge separation (Fig. 14, top). Under the assumption that charges are separated as long as the crack propagates we normalize the first signal rise to the maximum crack lengths as determined from post-mortem microscopy of the fracture surfaces. This results in a function for the time dependence of the crack tip position (Fig. 14, middle). The first derivative of this function then gives the time dependent crack velocity (Fig. 14, bottom). This method uses additional assumptions. We have to assume that the density of separated charges is in fact the same for every incremental crack surface area. Additionally, we have to assume that the polarisation of the net charge density does not change during the propagation of the crack. For this reason, it should be noted that this method only works with half of the recorded EME signals, i.e. those signals that show a distinct polarity. The presented result therefore only includes these signals.

For the PEEK specimens, where the crack propagates in two stages, we cannot normalize the maximum to the total crack length. For the different stages the ratio of the amplitude rises differs from the ratio of the crack lengths. This indicates a difference in surface charge density for the two stages. Therefore, the velocities were determined separately for each stage, as indicated in Fig. 15.

Table 3 summarizes the obtained maximum crack velocities v\(_{\textit{max}}\) for unstable crack growth for each polymer. For comparison, the transversal sound velocities v\(_{T}\) and the respective rayleigh wave velocities v\(_{R}\) are also given. These values were calculated using Bergman’s approximate [39], with the material parameters shown in Table 1. The obtained values for v\(_{\textit{max}}\) vary greatly for the different polymers, while all of the velocities are below the rayleigh wave velocities which define the upper limits for the crack propagation velocities in these solids.

For PEEK, the second stage of its fracture has the highest crack propagation velocity whereas the crack propagates much slower in the first stage.

Of all the tested polymers, PTFE features the lowest value for v\(_R\). This is reflected in the obtained crack propagation velocity.

No comparison is made to polymer crack velocities from literature since the crack propagation velocity depends on the local stress states and therefore on the specific specimen geometry as well as potentially existing residual stresses originating from the materials processing conditions. Nevertheless, the relation between the derived maximum crack velocities and the Rayleigh wave velocities indicate that the proposed approach could lead to meaningful crack velocity profiles.

The errors for the velocities given in Table 3 are the standard deviation derived from the averaging process. Additional error sources are the choice of the low pass filter frequency as well as the determination of the total crack length. Especially for the materials with partially ductile crack propagation the determination of the beginning of the EME signal generating brittle crack may prove challenging. These influences differ for the different polymers but are estimated to be of the same order as the standard deviation.