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Characterizing Carbon Content in Carbon Fiber Reinforced Plastics
Master thesis Physics and Astronomy: Science for Energy and
Sustainability
Christos Tsoulfas
Vrije Universiteit Amsterdam (VU) & University of Amsterdam (UvA)
Supervisor: Dr. Rudolf Sprik
Second reader: Prof. Davide Iannuzzi
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Abstract
The Eddy Current Testing (ECT) method is a well known electromagnetic technique for detecting changes and defects in conductive materials such as metals. ECT can also be used in materials with conductive components such as carbon fibers. Many sample plates are measured to validate ECT as a technique that can distinguish differences between materials due to their electrical properties. Because of their unique characteristics, the Carbon Fiber Reinforced Plastic (CFRP) plates are especially interesting candidates for the ECT. The results reveal that the thickness of the CFRP plates plays a crucial role both to the system’s resonance frequency and to the value of its mutual inductance. As the thickness increases, the resonance frequency seems to shift to slightly lower frequencies up to the point that completely disappears. For the rest of the samples, which are plastic plates with different metal coated patterns on their surfaces, ECT is able to distinguish each material as by placing each plate between the coils, the system has different mutual inductance versus frequency behavior. This outcome was expected, as the value of the mutual inductance is highly dependent both on the conductive content and on the spatial distribution of the conductive material in the sample. Therefore, the ECT technique can be used for detecting changes in the carbon content and in the metal content of each plate so as to qualify and, if possible to quantify, each defect.
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Table of Contents
1)
Introduction
2)
Theory
3)
Experimental set up and method of analysis
4)
Research in this thesis
5)
Measurements
5.1) Comparison between different samples
5.2) Measurements of TWCF Plates
5.3) Measurement of metallic coated plates
5.4) Measurement of prepeg plates
6)
Conclusion and remarks
7)
Acknowledgements
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1. Introduction
Carbon Fiber Reinforced Plastic composites are very durable and they have superior properties. The most important of these are that they are light weight, heat- and corrosion-resistant, they have high tensile and fatigue strength and there is high flexibility in tailoring the material for each application. The aforementioned properties make numerous industries interested in CFRP. Some examples of applications which already use CFRP materials are: the automobile industry’s BMW i3 all-electric car, the aircraft industry’s Boeing 787 Dreamliner and Airbus A380. Their properties renders them also
useful for some civil applications such as tennis rackets, fishing rods and wind turbine
blades[1],[2]. Figure 1.1 shows some of the applications.
Figure 1.1: Applications of CFRP, the first picture is Boeing 787 Dreamliner and second one is the BMW i3 all electric car.
The physical origin behind CFRP materials’ unique properties is based
on the combination of carbon
fibers(CFs) and matrix resin[1],[2]. The
electrical properties of CFRP materials are induced by a complex network consisting of CFs that are interwoven
with many unidirectional (or
directional) plies stacked together in various fiber orientations. Figure 1.2 illustrates the plies that create the
CFRP plate(called laminate). In
general, the CFs are separated by insulated polymers. However, some of
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points where the CFs are in touch. In the latter situation, wherein each ply has its own CF direction, the contact points are formed in the interface of the plies. Therefore, the bulk CFRP material contains some electrical networks that are formed by the CFs and
the contact points, which conduct electricity in the network’s direction[1]. However,
despite all these advantages, CFRP composites are vulnerable materials due to their laminated structure. They are prone to damages cause by fatigue and impact load that will result in strength degradation. Consequently, failures such as delamination, matrix cracks and fiber fractures may occur, among others[1],[2]. Figure 1.3 illustrates the most
common damages to the CFRP. Their carbon(“conductive”) content plays a crucial role to their electrical properties as their conductive content defines the parameters of the aforementioned electrical circuit. More specifically, there is a linear relationship between the number of contact points and the carbon content (with the carbon content being in linear relationship with the thickness of the sample). In addition, the spatial distribution of the carbon content inside each plate may produce different electromagnetic interference to the coils. There are also some other parameters that affect electrical properties of the CFRP materials that are mentioned in the next section.
Figure 1.3: Illustrations of the inflicted damages in the CFRP composites, a) is the Matrix cracking, b) is
the fiber breakage, c) is damage from low velocity impact and d) is delamination.[1]
There are many destructive testing(DT) and non-destructive testing(NDT) methods that are applied to inspect CFRP. Some advantages of the NDT versus the DT methods are that some of these NDT approaches can be applied to the entire process of CFRP the
manufacturing chain, thus leading to optimizations.[1] Additionally, use of NDT methods
can ensure that quality parameters are acquired, enabling reworking and repairing the
CFs preform.[1] Lastly, NDT methods allow on-time and on site measurements, which
save time and reduce cost.[1] One the whole, the results of NDT practices include less
waste of material and better control of the whole manufacturing process, which in turn
lead to stronger business opportunities[1]. Traditional NDT techniques include
thermography[3], acoustic emission[4], X-ray[5],[6] and Ultrasonic testing[8],[9]. Eddy Current
Testing is a simple, fast, real-time NDT electromagnetic technique which does not require contact. The detection of defects is achieved by measuring the change of the electrical conductivity. Information about the CFs’ distribution and texture can be acquired through a simple ECT scan. Moreover, many kinds of defects in CFRP can be detected with ECT, including CFs’ misalignment, gaps, cracks, missing CF bundles, delamination, and impact damages. More published literature regarding defect detection in CFRP is listed in this paper’s Reference section.
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2. Theory
ECT is a well-known inspection technique used for detecting defects in conductive materials. Quality parameters of dry multilayered carbon textiles and consolidated
material can be acquired[1]. This section will present the physical principles underling the
ECT testing[1],[16].
When a conductive material is in close proximity to an exciting coil with an alternating current running though the coil, then a changing magnetic field is produced in the axial direction of the coil. Inductive currents will be generated as a response to the applied
magnetic field inside the inspected material, as described in Faraday’s law. These
currents flow to the incident magnetic field. Then, according to Lenz’s law, these same currents create a secondary magnetic field which is opposed to the first in order to decrease the applied electromagnetic field. A schematic demonstrating the phenomenon can be seen in Figure 2.1. The above situation renders a change in the coil’s inductance (and hence, in its impedance). This change can be traced and measured to obtain information about the defects in the CFRP materials.
In general, ECT systems may consist of both excitation and pick-up coils or the same coil may be the used for both purposes[1],[12]. It is important to note the distinct
differences between CFRP materials and metallic plates. Metallic plates are homogeneous and hence a directional anisotropy in the plate does not exist. Contrastingly, CFRP composites are conductive due to the conductivity of the carbon fibers. The carbon fibers exist within the matrix creating an electrical network (as explain to the previous chapter). However, the presence of the non conductive polymer(between the plies) causes a much higher electrical resistivity in the direction perpendicular to the CFs than in the one that is parallel to them creating a directional electrical anisotropy.[1],[13]
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Moreover, as referred in the previous chapter, the electrical conductivity of CFRP relies on many different parameters, as the current flowing in the CFRP is highly depended on the number of the contact points among the CFs which again is depended linearly on the carbon content of the plate. Besides, there are some other parameters which affect the electrical conductivity such as the fiber waviness, the stacking sequence, the
temperature and the humidity, etc.[13] Lastly, the measured conductivity of a CFRP plate
is its bulk conductivity (average conductivity of the whole material) and not the conductivity at a specific direction[1],[13].
3. Experimental set up and method of analysis
The most efficient way to understand the conductivity of a system is by using a set of coil and measure the mutual inductance between these two coils. The mutual inductance
provides data that gives indications about the conductive material’s content and
information about its defects. To obtain the best data, the experimental set up needs to have the highest possible sensitivity to detect even the smallest changes. In this chapter, the experimental set up is introduced and its schematic can be seen in Figure 3.1. Then the system’s physics are explained.
Figure 3.1: Schematic of the experimental set up.
The red lines in Figure 3.1 represent connection cables. The whole set up consists of a personal computer(PC) connected to the impedance analyzer IM7581(HIOKI) and the keysight module U2751A. The HIOKI is essential in the experimental set up because it’s able to measure the system’s inductance. The keysight is another essential component of the experimental set up, the keysight is a switching device that is used to create the
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proper electrical circuit to obtain the desired measurements. Furthermore, the PC is used to control and save the experimental data with the use of the programming language Python. The PC also controls the keysight to create the necessary electrical circuit. The keysight’s interface can be seen in Figure 3.2.
Figure 3.2: Illustration of the keysight’s interface for creating the circuits for a) constructive interference and b) destructive interference.
U2922A, the keysight module is connected with keysight module U2751A and as it is a cable connector, it is needed for the hardware connection of the experimental set up. The set of the coils and the HIOKI is connected with that module in order to have a complete electrical circuit. In general, many different cable’s connections with different switches can be used in order to create the needed electrical circuit. The experimental set up used for this thesis is realized by connecting the HIOKI at the R3-R4 switches and the coils at the C5-C6 and C7-C8 switches, respectively. Finally, the grey line represents the sample (plate) which is placed between the set of coils. Numerous measurements can be achieved by choosing the proper set up in order to obtain the desired data set.
This situation’s experimental procedure is more complicated than that of the situation explained in the aforementioned theory. The physical difference produced by these two electrical circuits is illustrated in the next figure, Figure 3.3. The electrical currents running through the coils can either be in the same direction for both coils wherein constructive interference occurs (between the induced magnetic fields) or the currents can run through the opposite direction (creating destructive interference between the induced magnetic fields).
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Figure 3.3: Schematic illustration of the magnetic flux of constructive(left) and destructive interference(right).[16]
It needs to be noted that the proper device for measuring in the desired range of frequencies must be used. In previous studies is illustrated that changes in the CPRPs such as misalignments of the CFs or CFs breakage and matrix cracking produce a change in the system’s mutual inductance for the frequency range of 10kHz to 10MHz.[15],[16]. In the case of
this experiment, a frequency range of 100kHz to 2-4MHz proved to be sufficient for obtaining the desired data. The keysight is able to perform as a switching device properly on that frequency range. However, previously, another device had been used as a relay for creating the electrical circuits which did not measure reliably on that range of frequencies. The previous device that was used as switches in experimental circuit can be seen in Figure 3.4.
In broad strokes, the experimental circuit can be represented as an RLC circuit (connecting a resistor (R), an inductor (L), and a capacitor (C)). Hence, the analysis of the measurements should also be able to be represented in this manner. Practically, this means that in the method of the analysis, a number of parameters need to be considered to represent physical phenomena. Firstly, depending on the coils, there is a self-resonance frequency and some induced capacitance due to the wiring of the coils, the values of the self-resonance frequency and the mutual inductance between the coils
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are depending on the shape of the coils, the thickness of the wires, and the number of turns the coil has[16]. Depending on the specific properties of each sample such as its
thickness and its conductivity, different values of resistance, inductance and capacitance need to be used as parameters in the electrical circuit to act as the material’s properties. Figure 3.5 illustrates the elementary RLC circuit. In the bulk material(plate/laminate), this
elementary circuit is repeated and it is connected both in series and in parallelto itself.
Figure 3.5: Elementary electrical circuit.[1]
In addition, if more than one plate is placed between the set of coils, a number of parameters can alter the outcome of the measurement. These parameters include whether the plates are in contact or not, and if not, what is the distance between them. This may alter the system’s resonance frequency and its value of mutual inductance by
inducing another “extra” capacitance. The spatial distribution of conductive component
(CFs or metals) in the sample can cause a number of similar changes.
As described in the HIOKI manual, the experimental mutual inductance(Lmut) can be deducted as:
Lmut = ( Lconst – Ldest ) / 4 .
Where Lconst is the constructive and Ldest is the destructive inductance. Both are
dependent on the two settings of the switching device. By using the equation above, the
mutual inductance can be deducted for each measurement. However, the system’s
resonance frequency cannot be deducted in such a simple matter. The system’s resonance frequency depends on many parameters such as the self-resonance frequency of the coils, the material which is placed between the coils, and the spatial distribution of the material’s conductive component. The number of plates that have been placed between the coils and the overall thickness of the sample, the placement of the plates between the coils, if the plates are 100% identical etc, are all important
parameters that affect the system’s behavior. These parameters cannot permit you to
claim absolute statements that are dependent on only one parameter. However, many indicators can be seen such as changes in the capacitance of the system which can be again happening for numerous reasons as explained above. Moreover, the general expectation is to be able to distinguish differences/defects that can cause a change to the system’s conductivity that is in the range of μH. This will give a clearer understanding of the full circuit which is needed to be able to achieve more quantitative measurements
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of the resistivities. As this is achieved, measurements without doing a calibration with standard well-characterized plates will be possible leading to reducing the needed experimental steps thus reducing the amount of time that the whole process of the experiment takes. In addition, some other experimental work has already been published with a detailed analysis on the aforementioned parameters such as which set of coils
was used, the distance between the coils, the used voltage etc.[16]
In the case of this experiment, the analysis, which is dependent on the above formula, can only be valid for the range of frequency which is as far away as possible of the self-resonance frequency. For results which correspond to physical phenomena near the self-resonance frequency a clear statement cannot be done. Modeling the mutual inductance behavior versus frequency by an RLC digital circuit could provide a guideline for the values near the self-resonance frequency and hence be able to make clearer statements. However, this is not the research study of this project.
4. Research project of the thesis
The main research concern of this thesis is to validate the ECT technique as a promising method for detecting changes and defects in CFRP plates as well as a method that can be used for quantitative measurements. Thereafter, the goal is the understanding of the
physical origin of the defects to be able to model the system’s mutual inductance
behavior (of each material) depending on the inflicted defect. The final goal is to achieve a quantitave analysis depending on each defect. The qualitative analysis had already
been achieved by the N. Roos and Y. Zandbergen who are HvA’s students. However,
they had used one coil (both as excitation and pick up coil). In this research project, the aforementioned settings will be used to obtain data that will permit a quantitative analysis.
However, as there was not enough experimental time, the acquired data was not enough for realizing all the goals, but the validation of the ECT technique was managed to be done with the current data.
5. Measurements
5.1 Comparison between different samples
The first measurements concern the mutual inductance versus frequency behavior for different samples. They can be seen in Figure 5.1.2. The goal of these measurements is to prove that different samples can be distinguished due to their unique electromagnetic properties. It needs to be stated that each plate has its own morphology as far as the
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carbon fibers or the copper coating is concerned. The composition of some samples can be seen in Figure 5.1.1.
Figure 5.1.1: Illustration of samples, 01 is a full metallic plate, ED03 is a plastic plate with copper coated wholes and horizontal and vertical lines and Frank is a CFRP plate made by the HvA students.
Table 1 shows the name and the type of the sample plates and the corresponding color of each measurement. A small explanation concerning the samples can be found after the table.
Table 1: Sample plates placed between the set of coils.
Color of measurement Name of Plate Type of plate
Black - Only coils (reference signal)
Green Plate.02 Copper coated transparent holes
Orange Plate.03 Copper coated transparent holes and
Vertical and horizontal lines
Yellow Plate.AA3124 Prepeg ply
Purple Plate.Frank Twill weave CFRP (HvA students)
Red Plate.Henk Twill weave CFRP (HvA students)
Blue Plate.01 Full metal plate
The reference signal, which is depicted by the black curve in Figure 5.1.2, is the signal induced without a sample (plate) with the use of only the coils. The distance between the coils was 12.5mm and its coil has an inductance of 24μΗ.
Regarding the samples, plate named Plate.01 is a full metal plate while the plates named Plate.02 and Plate.03 are made from polymers(plastic) and they have different patterns of copper coating on their surface. More specifically, Plate.02 has transparent, copper coated holes and Plate.03 has both transparent holes and vertical-horizontal
lines(named “islands”) that are copper coated. As the number of CFRP was limited, the
metallic plates were used as well-specified complex structures that could mimic CFRP. The plates named Plate.Frank and Plate.Henk are TWCF test-plates with no substantial carbon fiber morphological difference. These two plates were made and named from
HvA students[17] and the plates’ names were maintained throughout this project out of
respect for the students’ efforts. Finally, the plate named plate.AA3124 depicted in orange color, is a thin carbon fiber film (called as “ply/prepeg” in the previous sections) used in the manufacturing procedure of TWCF plates. Figure 5.1.2 illustrates these measurements.
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Figure 5.1.2:Mutual inductance versus frequency for five different plates. The plates have morphological
differences.
In Figure 5.1.2, it can be seen that the system’s resonance frequency for these five
cases does not remain the same. Another remark is that by placing the Plate.01, Plate.Frank and Plate.Henk between the coils, the system seems not to have a resonance frequency and the mutual inductance is almost a flat line around the value of zero. However, by placing Plate.02 (green line) the system has a resonance frequency at 1115 kHz (for the positive peak) and 1220 kHz (for the negative peak) and by placing Plate.03 (orange line), the system has a resonance frequency at 1132 kHz (for the positive peak) and 1295 kHz (for the negative peak). The crucial remark is that even for the two plates in which the system has a resonance frequency there is a drop in the value of mutual inductance. From 200 μH which is the reference signal (black curve) to
160 μH (by placing Plate.02) to 110 μH (by placing Plate.03). It goes without question
that depending on the plate the system produces different values both for the mutual inductance and the resonance frequency. By comparing the results of placing the plate.02 and the plate.03 it can be stated that spatial differences on the copper coated
surface are able to reduce substantially the absolute value of the system’s mutual
inductance. Also, the resonance frequency has undergone a small change. This means that changes depended on the spatial distribution of the copper(metal) on the copper coated substrate can be detected and hence evaluated. The same can be illustrated by comparing the results of the measurements in which the system seems not to have a resonance frequency and there are small differences/changes in the value of the system’s mutual inductance. Figure 5.1.3, provides a zoom-in for the measurements of the plates: plate.Frank, plate.Henk, plate.01, and even the measurements of the plates: plate.Frank(purple line) and plate.Henk(red line) which are both TWCF test-plates with similar carbon fiber morphology and thickness, some differences can be illustrated.
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Figure 5.1.3:Mutual inductance versus frequency for three different plates.
The behavior of the system’s mutual inductance dependent on the frequency is the same for both the TWCF plates with small differences on the value of the mutual inductance. This proves that the ECT technique can be used for detecting small changes on the system’s conductivity even among plates which are consisted of the same material with the same morphology.
5.2 Measurements of TWCF Plates
The next samples that were tested were the Twill Wave Carbon Fibers (TWCF) test-plates bought from the PROTECH COMPOSITES company. All the test-test-plates have exactly the same morphology but differ in thickness. A picture of these samples can be seen in Figure 5.2.1.
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Figure 5.2.1: Test plates of carbon fiber reinforced plastic.
Measurements that include samples of a high thickness (1.95mm and higher), more than one test-plate was used.
Figure 5.2.2: Mutual inductance versus frequency for thirteen different thicknesses of TWCF plates.
In Figure 5.2.2, it can be seen that there are differences both in the system’s resonance frequency(a small shift) and in the value of the mutual inductance depending on the
sample (sample’s thickness and hence, carbon content). By comparing the reference
signal which is the signal that is produced by measuring the system’s conductivity, of only the coils(black line) with the signal of the system by placing the TWCF plate of 0.25mm thickness (purple line), both the above statements are illustrated. The system’s resonance frequency undergoes changes from 1245kHz (high peak) and 1375kHz(low peak) to 1132kHz and 1482kHz, respectively. Also, the value of the mutual inductance
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does not remain constant. The maximum value of the mutual inductance is 140 μH
(reference signal) and it can be seen that by just placing a TWCF plate of a thickness of 0.25mm in between the coils, is decreased, reaching 40μH. That is a change of one order of magnitude. In general, as the thickness of the measured sample increases, the absolute value of the mutual inductance tends to be minimized reaching the value of zero as the mutual inductance curve almost becomes a flat line. This can be better seen in the next figure, Figure 5.2.3, which is the same figure but with the reference signal subtracted so as to have a closer look at the graph.
Figure 5.2.3:Mutual inductance versus frequency for thirteen different combinations of TWCF plates. The
plates have the same morphology.
From Figure 5.2.3, the comparison of the mutual inductance and the resonance frequency depending on the thicknesses of the samples is clearer than that in the previous figure. By comparing the measurements by placing the TWCF plates of a thickness of 0.25mm and 0.50mm, it can already be seen that the system’s resonance frequency is changed and the value of the mutual inductance has also decreased. As, it
is expected from the theory[15], there is a linear relationship between the sample’s
thickness and the system’s value of the mutual inductance (for CFRP)[15], for metals, the
situation is different. The clearest outcome can be seen by comparing the reference signal with the signal of the plate of 5.50mm. For the measurement of the plate with the thickness of 5.50mm the mutual inductance remains almost constant at the value around the zero for any frequency. This practically means that there is no mutual inductance. These measurements prove the validity of the measurement’s method for detecting changes both on the system’s mutual inductance and the system’s resonance frequency for the same material depending on its thickness.
However, as discussed inthe chapter of experimental set up and method of analysis, the
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capacitance induced by the method of the experiment interferes. At the edges of the frequency range, where the resonance frequency has minimum influence in the whole behavior of the system’s mutual inductance, a clearer view can be seen. The following
figure, Figure 5.2.4, shows the system’s mutual inductance versus different values of
thickness by choosing specific frequencies.
Figure 5.2.4:Mutual inductance versus frequency for thirteen different thicknesses of TWCF plates. The
plates have the same morphology.
In Figure 5.2.4, it can be seen that measurements which include plates of a small
thickness (up to 1.50mm), as the frequency is getting increased the value of the mutual inductance also increases. However, for higher values of thicknesses the opposite is happening, the mutual inductance is getting decreased. In addition, it seems to be another important result. The value of the mutual inductance has a sharper decrease for the higher frequencies. This result can be used for detecting changes by optimizing the frequency depending on the thickness of the sample (for that range of frequencies and thicknesses). On that way, the system can be optimized depending on the sample. Another idea would be to model the behavior of the whole system, including the self-resonance of the coils for the whole range of frequencies so as to have a clearer view on which parameter affects the most the system’s mutual inductance.
5.3 Measurement of metallic coated plates
The next samples are metallic- (copper-) coated plates. As the number of the CFRP plates was limited, metallic plates were used so as to imitate the CFRP behavior. An analogy between the CFs content and the metal content can be made as both of them
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are conductive materials. First of all, each measurement has its own setting (depending on the placement of the plates. These different placements/settings need to be explained. Face to face configuration is the case in which the front surface of one plate is in contact with the front surface of another plate (hence, the conductive material of each plate is in contact). Face to back configuration is the case in which the front surface of one plate is in contact with the back surface of another plate. Also, in the case in which there are three plates, the two of them are face to face and then the front surface of the third plate is in contact with the back surface of one of the other two plates. In addition, for the two cases in which there are four plates, in the first case the plates are per pair face to face and then the two pairs in contact. In the second case, the front surface of each plate is in contact with the back surface of another plate. Figure 5.3.1 illustrates the measurements.
Figure 5.3.1: Mutual inductance versus frequency for six different cases, the black line represents the
mutual inductance for one plate, the blue for two plates, the green for 3 plates, the cyan for 3 plates, the magenta(purple) for 4 plates and the red for 4 plates.
There are many conclusions that can be drawn from Figure 5.3.1. Firstly, the system’s
resonance frequency for these six cases does not remain the same. Secondly, there is
not an analogical response in the system’s resonance frequency and in its mutual
inductance depending on the number of the plates (and hence the sample’s thickness).
However, there are some similarities that can be stated. The system’s resonance
frequency has similar values for the cases of: one plate (black line), two plates in face to face configuration (blue line), three plates (cyan line) and finally for the two cases of the 4 plates. In addition, the largest difference for the resonance frequency is reported for the case of two plates in face to back configuration (green line) compared to the two plates in face to face configuration. As the metal content is the same for both measurements and the only thing that has changed is the positioning of the plates, the
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change on the value of the resonance frequency may be explained as induced capacitance depending on the distance between the metallic coated surfaces.
The most important unexpected conclusions are that the system’s resonance frequency
and its mutual inductance do not an analogous change dependent on the sample’s
thickness. This may be an indication of extra capacitance. As the metal coated surfaces is not in contact with each other it can be argued that this is not a measurement of one thick plate but a measurement of two plates with some mm distance between them. However, that should also be valid for all the other cases in which there is more than one plate in face to back configuration, as the physical reason which produces that extra capacitance remains there.
These measurements are not tested for their reproducibility as there was not enough lab-time. It is suggested to remake these measurements and then state actual results and remarks, if possible with more plates and more configurations(placements of the plates).
5.4 Measurement of prepeg plates
The next samples were thin films(“prepeg plies”) which are used in the manufacturing process of the CFRP. An image of these prepeg plies can be seen in Figure 5.4.1, in which the front and the back side of the prepeg is illustrated.
Figure 5.4.1: Image of prepeg plate. The black color is the front side and beige color is the back side of the plate.
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The CF’s direction is the same for both the plies. This means that by positioning them face-to-face or face-to-back, a spatial anisotropy can be created. By comparing these two scenarios the behavior of the mutual inductance versus the frequency depending on the anisotropy can be seen. The next figure, Figure 5.4.2 shows the mutual inductance versus frequency behavior for three different cases/placements. The black curve corresponds to the measurement of one ply placed between the coils and the blue and the green lines correspond to the measurements of both the plies placed between the coils with different orientations. The configurations have been explained into the previous chapter.
Figure 5.4.2:Mutual inductance versus frequency for three different cases, the black line represents the
mutual inductance for one plate, the blue line for two plates and the green line for two plates with different configuration.
In Figure 5.4.2, three different conclusions can be seen. Firstly, the system does not
have a sharp resonance frequency and they may be two or more resonance frequencies around 1500 and 2500 kHz. Secondly, the mutual inductance curve seems to have similar behavior for both configurations in which there are two plates. The difference is that the absolute value of the mutual inductance is the same around 1500kHz and different around 2500kHz. As there is no change in the carbon content and there is no damage inflicted in the plates (that could produce a morphological change into the plates), this result can be interpreted as another morphological result (depending on the positioning of the plates). That change causes different eddy current distributions. Hence, in this case, the change in the system’s conductivity and its resonance frequency is highly affect by the plate’s positioning.
In addition, as the mutual inductance versus frequency behavior change is really small, it would be wise to make more measurements with the same settings and with more samples(prepeg plies) to validate the results by reproducibility. An analogy between the
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sample’s thickness and the system’s resonance frequency which cannot seen with the current data, may also be found. Lastly, comparing all configurations with the reference signal(which is the measurement of only one ply), it goes without question that the absolute value of the mutual inductance is getting affected for all frequencies in the range 100Hz-2500kHz.
6. Conclusions and remarks
First of all, it is proven that ECT can be used for detecting changes and differences depending both on the material and on the spatial distribution of the sample’s conductive component, as shown in Figures 5.1.2 and 5.2.1. In addition, the change of the absolute value of mutual inductance depending on the carbon content (for the same material) has also been illustrated in Figure 5.2.2. The carbon content of CFRP is in linear relationship with their thickness. Thus, as the thickness of the CFRP increases, the carbon content is
reaching higher values. As the carbon content(sample’s thickness) increases, the
absolute value of the mutual inductance is decreasing and tends to reach the value of zero both for the whole range of frequencies (from 100kHz to 2MHz). However, the physical origin of this drop cannot be described by a simple model which has only the CFRP’s thickness as a parameter. Induced capacitance between the interfaces of two (or more) plates seems to be created. The physical origin of this induced capacitance varies depending on the sample. The measurements that include two or more CFRP test-plates to increase the sample’s thickness, include also more than one interface leading to a complex system. This situation affects the whole system’s behavior. By comparing CFRP samples of different thicknesses at specific frequencies (far away from the system’s resonance frequency) as shown in Figure 5.2.4, a number of results have been illustrated. For low thicknesses (up to 1.50mm) higher frequencies seems to produce higher values of mutual inductance. Also, as the sample’s thickness increases the drop of the value of the mutual inductance is having a sharper decrease for the higher frequencies. These results can be used for in-site measurements and for calibrating the measurement’s device to reach the best possible measurement.
Furthermore, from Figure 5.3.1 more indicators of what can cause shifts to the system’s resonance frequency and changes in its mutual inductance behavior can be stated. Capacitance induced by the different positioning of the metallic-coated surfaces seems to be the culprit. When the metallic-coated surfaces are not in contact, the conductive components of the plates have some mm distance to each other. Possibly, this situation is creating another capacitor. However, these measurements need to be tested again to validate this result. If these results are indeed valid, then the shift of the resonance frequency can also be used for detecting specific defects such as delamination. Future research should involve analysis depending on the carbon fiber or the metal coated content/density. The ideal result would be able to model the behavior of the mutual inductance depending on the presence (volume or weight) of carbon fibers or metals.
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Well defined human defects inflicted in the plates can be used as samples (in which the percentage of the missing volume to volume or weight to weight carbon fiber or metal would be known), 10%, 20%, 30%, 40% and 50% missing carbon content would be enough to realize a quantitave approach. Pilot cases, such as the EDDY mouse could reach higher sensitivity and hence, be able to detect even the smallest defect(not visible defect).
Another experiment would be to keep the missing carbon fiber content constant and change the spatial shape of the defect ( holes versus lines or even transparent hole versus 2 or 3 holes or lines which are not transparent) and then compare the results. In all the above situations/experiments, the eddy currents distributions (and hence the system’s conductivity will be altered) providing new data that will illustrate a clearer picture of the system’s correspondence depending either on the “missing” carbon content or on the spatial difference of the defect. Furthermore, another approach would be to change the experimental setting (change the shape of the coils) and repeat the same measurements to check if more useful data can be obtained. This would be helpful, as by choosing the proper shape of the coils, the desired (anisotropic) magnetic
field would be produced to distinguish changes in the system’s conductivity, depending
on the shape of the defect.
As the eddy currents distribution is analogue to the contact points of the carbon fibers these experiments would help to model the behavior of the system’s mutual inductance versus frequency depending on each situation/experiment. For the metallic coated plates the same cases could be applied. In addition, as there are already plates which have metallic-coated patterns on their surfaces, the defect would be to create a “missing” copper coated hole or a number of holes or a missing island or a number of islands, and describe the change on the behavior of the mutual inductance versus both the shape of the defect and the missing metal content. However, this is a complicated issue, because modeling the behavior on the system’s mutual inductance cannot be achieved by considering changes that involve just one parameter, (as explained in the previous chapters), two or more parameters need to be considered to model the desired behavior. Another easier approach would be to use as samples the plates which have their whole surface copper coated and then have a well defined defect such as a transparent hole in which the missing copper content would be known. Then, as the defect would be
well-defined, the data’s analysis would be easier. In addition, a change in the hole’s radius
can be made (creating different defects/ more samples) to produce more data. Then by comparing the results of the measurements that have the same missing metal/CFs content but different spatial defect, a better understanding of the eddy currents distribution can be illustrated. In any case, the system’s self-resonance frequency needs also to be considered to model the system’s mutual inductance for the whole range of frequencies. All the aforementioned experiments will produce knowledge that will permit
the categorization of the parameters that affect the behavior of the system’s mutual
inductance versus frequency (induced capacitance, missing conductive material or different spatial distribution of the conductive material) according to their significance, thus ensuring that the system is as optimized for the desired application as possible. All the obtained knowledge can be used for creating new-generation (conductivity’s) sensors that will lead to stronger business opportunities.
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7. Acknowledgements
Foremost, I would like to thank Dr. Davide Iannuzzi for introducing me to the D-lab of the Vrije Universiteit van Amsterdam(VU) and give me the opportunity to collaborate with one of their teams as well as agreeing of being the second reader of my thesis. I would like also to express my gratitude to Dr. Rudolf Sprik who accept me as a member of his team and gave me crucial advises as my daily supervisor. Finally, I would like to thank Dorien Verhoeven who helped me to grand access to the D-lab facilities during the current covid-19 health crisis in order to be able to finish my thesis in time.
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