Quantitative Penetration of Eddy Currents in Carbon Fiber
Reinforced Plastic
David Langhorst July 30, 2019
Abstract
Eddy current testing has found to be useful to quantitatively determine the penetration and the conductivity of CFRP’s. In this thesis the penetration of CFRP’s is
measured by looking at the transmission of the magnetic field through a CFRP plate. An alternating system of two coils, a receiving one and transmitting one, create eddy
currents on the CFRP’s surface. The eddy currents induce a magnetic field in the opposite direction. The resultant magnetic field measured in the receiving coil is a measure for the penetration through a CFRP plate. Increasing the alternating oscillator’s frequency shows decrease of the penetration through a CFRP plate. The frequency increase shows an increase of electrical conductivity of the CFRP material.
Student-number 10534865
examiners R. Sprik & D. Iannuzzi
course Bachelor project Physics and Astronomy Assignment Bachelor project
Version Final
Contents
1 Populaire samenvatting 4
2 Introduction 5
3 Theoretical background 7
3.1 DT and NDT . . . 7
3.2 Eddy current testing . . . 8
3.2.1 Physics behind eddy currents . . . 9
3.3 Carbon Fiber Reinforced Plastic . . . 11
3.3.1 Electrical Conductivity . . . 12
3.3.2 Damages . . . 12
3.4 Skin Effect & Skin Depth . . . 13
3.5 Conductivity . . . 15
4 Method & set-up 16 4.1 Equipment . . . 16
4.2 Measuring method . . . 16
5 Results 18 5.1 Magnitude scanning . . . 18
5.2 Skin depth results . . . 19
5.3 Conductivity results . . . 21 6 Discussion 23 7 Conclusion 24 8 Acknowledgement 25 9 Bibliography 26 10 Appendix 28
List of Figures
1 Comparison of major NDT methods (Lin, X., 2012) . . . 8 2 The coil (blue) with coil’s magenetic field (red). The eddy currents on the
sur-face (green) with the eddy currents’ induced electromagnetic field lines (purple) in the opposite direction of the coil’s (Texas Instruments, 2015). . . 9 3 Lamina vs. Laminate (Lin, X., 2012). . . 11 4 Forms of delamination (Menana, H.,11 Fliachi, M., 2009). . . 13 5 Texas Instruments coils in green on the left. The Analog Discovery 2 on the
right side in the figure with wires connected from the AD2 to the coils. Between the coils is a gap where in between the CFRP plates are placed. . . 17 6 Measuring set-up top view . . . 17 7 Log scaled frequency in Hz with magnitude in dB. Legend labels the plate
thickness. . . 18 8 Linear scaled frequency in Hz with magnitude in dB. Legend labels the plate
thickness. . . 19 9 The skin depth as function of the frequency for different CFRP plates. The
legend labels the plate thickness. . . 20 10 The CFRP plates with different thickness are plotted against the magnitude in
dB. The higher the frequency steeper the slope. Legend labels tested frequencies. 20 11 The conductivity of the CFRP plates are increasing when the frequency
1
Populaire samenvatting
Tegenwoordig kan men op verschillende manieren onderzoeken of materialen wel of niet veilig en verantwoord zijn om te gebruiken als onderdelen in bijvoorbeeld de vliegtuig- of auto-industrie. Dit kan op twee verschillende manieren getest worden. De ene methode is door het te onderzoeken onderdeel te demonteren of kapot te maken (destructive testing (DT)). De andere methode is het door het te onderzoeken materiaal intact te laten (non-destructive testing (NDT)).
In dit onderzoek wordt er gekeken naar een NDT methode. In deze methode worden oppervlaktestromen oftewel ”eddy currents” gebruikt om te kijken wat de kwantitatieve in-dringdiepte is van de gegenereerde magneetvelden in carbon fiber materialen. De methode ”eddy current testing”, die al decennia bestaat, is veel getest op goed geleidende materialen zoals metalen. In dit onderzoek wordt gekeken hoe het carbon fiber materiaal zich verhoudt tot de al eerder onderzochte metalen.
Eddy currents ontstaan als volgt: Een of meerdere spoelen genereren op het moment dat er stroom doorheen loopt een magneetveld. Het magneetveld, dat in de buurt staat van een geleidend materiaal, genereert oppervlaktestromen op het oppervlak van het materiaal. Deze oppervlaktestromen genereren zelf ook een magneetveld dat in de richting van de spoel staat. Aan de hand van de verhouding tussen het gemaakte magneetveld van de spoel en het doorgelaten magneetveld gemeten achter het carbon fiber kan bepaald worden wat de indringdiepte is van magneetvelden in carbon fiber materialen.
Uit de resultaten is gebleken dat de indringdiepte van magneetvelden in carbon fibers veel dieper doordringen dan bij sterktere geleidende materialen zoals metalen. Ook is gebleken dat de geleidbaarheid van carbon fiber materialen zich anders gedraagt dan conventionele metingen met metalen.
Verder is uit de resultaten gebleken dat het testen aan de hand van eddy currents een goede methode blijkt om onderzoek te doen naar de structuur van carbon fibers. Dit kan geconcludeerd worden aangezien de magneetvelden diep genoeg kunnen doordringen door het carbon fiber materiaal.
2
Introduction
Carbon fibre reinforced plastic (CFRP) is widely used in the aircraft, windmill and automotive industry. In order to ensure that the CFRP is used under the right conditions, it is necessary to look for appropriate methods to safeguard these conditions. One has two options to ensure the safety of the materials. Destructive testing (DT) and non-destructive testing (NDT) are two different ways to investigate the component which are both compatible for CFRP materials. NDT means one does not have to dissemble the object that needs to be examined. However, all NDT methods out there have their own limitations. A number of research methods are ultrasonic NDT, X-Ray inspection, thermography, and Eddy Current Testing (Li, X., 2012).
The last research method will be discussed in this thesis. Eddy current testing is nor-mally used on conductive metals. Eddy currents are loops of electrical current induced within conductors according to Faraday’s law of induction. The currents flow in closed loops per-pendicular to magnetic fields which induce those electrical currents. The difference between CFRP and metals is that metals have a significant higher conductivity than CFRP and a lower eddy current penetration depth. Testing with eddy currents have showed to be very useful in comparison with other NDT methods. It is fast and simple. In comparison with other non-destructive methods, it is also cheap and efficient. The instruments that make and measure eddy currents provide insight into the material. The tests are also non-contact (Li, X., 2012).
CFRP is an extremely strong and light composite which contains carbon and epoxy poly-mer. CFRP’s are used wherever high strength-to-weight ratio is required. The fibres are bundled together to form a piece of rope, which can be woven into a fabric or laid down unidirectionally to form a lamina. The fibre in a directional way contributes to the value of the composite electrical conductivity σ. Which is much higher in the fibre direction and lower in the perpendicular direction (Lin, X., 2012).
Eddy current testing has a few limitations. One of these limitations has to do with the penetration depth of the magnetic fields induced by the eddy currents itself. This penetration depth depends on the conductivity σ of the CFRP and the frequency of the alternating current that the coil generates. The coil itself and the electrical circuit will also have to be analyzed to find out what the specific penetration depth of CFRP is. This is necessary to find out
whether it is possible to determine on the basis of eddy currents if there are any cracks and flaws in the material that can not be measured from the outside. If the penetration of the magnetic field is deep enough, then eddy current testing can be used as a research method to safeguard the safety of components in the car, wind and aircraft industry when the industries start making everything of this very hard and light composite material.
3
Theoretical background
Cracks and flaws can appear in the manufacturing process of CFRP or when the CFRP is in use. These defects can cause a rgeater risk of failure because it loses strength (Burdekin, F.M., 1990). To test and investigate if the CFRP is intact, there are different methods to investigate the safety and ensure the reliability. As Burdekin cited: “Defects indicate the group of imperfections which can make the component defective” (Burdekin, F.M., 1990). Under flaws one means an imperfection which is classified to be non-rejectable.
3.1 DT and NDT
As written in the introduction there are two ways to investigate components of products which are simply destructive and non-destructive testing. Destructive testing (DT) is described as a method whereby the part is removed from the original product in order to get the maximum amount of information. After the test the component is unusable because it is deliberately broken. With destructive testing it is possible to simulate the environment to get specific results. DT can also provide access to the objects inner structure which is one of the very hard things to obtain information from with NDT (Lin, X., 2012).
“Non-destructive testing is a form of testing, examination or evaluation made on an object to study the absence or presence of conditions or imperfections that possibly make an impact on the function of serviceability of the objects in the way that will not cause any kind of change or alteration on the performance of the object” (Hellier, C., 2001). So NDT has an advantage over DT because the components under investigation remain in their original form. NDT is often faster and cheaper than DT and methods show to be very useful (Lin, X., 2012). Scruby & Colbrook showed that a variety of NDT methods are also portable and in general the costs are lower. (Scruby, C. B., & Colbrook, R., 1992).
The main reason why one will use NDT is because it will increase the serviceability of components of specific materials which can cause malfunction of defects. As said above some of the NDT are portable to use and give information into the compontents’ structure, unscheduled investigations are easy to carry out when the parts are still attached (Lin, X., 2012). The specific NDT that will be discussed in this thesis is eddy current testing due to its advantages over other NDT methods in the application of the aviation industry and windmill industry.
Figure 1: Comparison of major NDT methods (Lin, X., 2012)
3.2 Eddy current testing
In general, an alternating coil produces magnetic fields close to a conductive material (in range of the diameter size of the coils). Because of the changing magnetic fields an electrical current (eddy currents) will be induced perpendicular to the magnetic fields on the conductive surface and induces it’s own magnetic field in the opposite direction. Eddy current testing is one of the most extensively used non-destructive techniques for inspecting electrically conductive materials at very high speeds that does not require any contact between the test piece and
the sensors (Papadakis, E. P., 1993).
3.2.1 Physics behind eddy currents
A coil in an electrical circuit creates a magnetic field by Faraday’s law of induction. It’s a basic electromagnetic law that predicts in what direction the magnetic fields will flow. Again, from Faraday’s law the induced magnetic fields themselves induce electrical closed loops of current. By Lenz’s law, the induced eddy currents will be in a direction that it will counter the magnetic change of flux. The magnetic field of the coil will be in a downward direction so the magnetic field induced by the eddy currents will be in an upward direction. From Faraday’s law and simple electromagnetism the eddy currents will flow counterclockwise as one can see in Figure 1 (Giancoli, D.C., 2008). Both the original magnetic fields and the induced magnetic fields due to eddy currents sum up to total magnetic field lines that can be detected in a receiving coil. Figure 1 below shows a simplified image of generated magnetic field by the coil and the induced magnetic field due to the eddy currents.
Figure 2: The coil (blue) with coil’s magenetic field (red). The eddy currents on the surface (green) with the eddy currents’ induced electromagnetic field lines (purple) in the opposite direction of the coil’s (Texas Instruments, 2015).
When one is working with materials that are subject to electric and magnetic polarization there is a more convenient way to write the information in an adjust form of Maxwell’s equations. Faraday’s law and ∇ · B = 0 are not affected between free space and non-free space. B is the magnetic field and E is the electric field (Griffiths, D. J., 2014).
∇ · B = 0 (1)
∇ × E = −∂B
∂t (2)
Maxwell’s equations in matter that are affected by in non-free space are the divergence of E into equation (3). Here D equals: D = 0E + P . P is the polarization.
The curl of the magnetic field of Maxwell’s equation in matter become equation (4). The B sign changes to H where H = µ1
0E − M . Here is M the magnetization (Griffiths, D. J., 2014).
∇ · D = ρf (3)
∇ × H = Jf +∂D
3.3 Carbon Fiber Reinforced Plastic
Carbon Fiber Reinforced Plastic (CFRP) is a strong and light plastic with carbon as com-ponent for the fiber material and other polymers at a macroscopic scale (lin, X., 2012). The strength-to-weight ratio is much higher when the materials are woven and pressed together (Heffernan, C. P., 1997). Because the CFRP is stiff, light and strong its excellent to use for aerospace and automotive industries (De Goeje, M. P., & Wapenaar, K. E. D. (1992). Just as other materials, cracks and flaws can occur in CFRP during service of the component when used. When CFRP will be used as a wing skin for example, one has to find these defects before malfunctions occurs. To ensure that CFRP can be used safely as material, one has to look preferably in-service and non-destructive to investigate that there is no cause for mal-function. Cracks and flaws will cause a loss of strength. Therefore, it is necessary to know how CFRP’s are made with all the features that entails.
The fibers are in the form of woven threads containing up to 104fila ments. These filaments are typically 7 to 15 µm in diameter (Lin, X., 2012). The CFRP’s are made when the woven threads of carbon fibers are embedded in a polymer, commenly epoxy and then pressed together into a layer. The component has low stifness and low strength and it contributes to the shape of the component. A single layer of CFRP is 0.05 − 0.2mm thick. In order to obtain components that can be used for mechanical purposes, layers need to be stacked onto each other to form a lamina. When the layers are all stacked in the same direction the lamina is called unidirectional laminae. When stacking laminae onto each other in different directions its called a laminate (Lin, X., 2012). The fiber directions are chosen to fulfill their mechanical purpose. To make the laminate, one needs to spread the fibers then the layers are stacked in a mould together with the liquid epoxy. With controlled temperature and pressure conditions the fibers and the epoxy will all together form the CFRP (Lin, X., 2012). See Figure 3.
3.3.1 Electrical Conductivity
The electrical conductivity value σ of CFRP is overall significantly lower than the conductivity of metals. Also the electrical conductivity properties of CFRP differ considerably from metals. There is a difference in orientation of electrical conductivity σ. Metals have the same σ in each direction of measurement. Copper has a σ -value of 5900 · 104 S/m and aluminum 3500 · 104 S/m (Siemens per meter). For CFRP’s it is different because CFRP has a high anisotropy. This means that the σ-value varies when one measures perpendicular to the unidirectional direction of the CFRP than when one measures parralel to the unidirectional direction (Lin, X., 2012). The value of σ parallel = 0.9 - 1.5·104S/m and the value of σ perpendicular = 0.01 - 0.2 ·104 S/m. So the electric conductivity value of CFRP is lower than metals by a factor of more than a thousand times. The electrical current that flows through the CFRP can only move between the carbon contact points from fiber to fiber. The material’s surrounding is just non conductive epoxy. The total impedance is the impedance of all the single fibers together (Lin, X., 2012). This implicates that a higher resistance than normal can indicate a crack or flaw in the component (Finlayson, et al., 2000). This can be used for detection of malfunction in the components.
3.3.2 Damages
The CFRP can be fabricated in different ways to serve different purposes. This means that different types of defects can also arise from these ways during fabrication or while using the CFRP. It is important to be able to distinguish these defects from one another in order to guarantee the safety of the component. The following are examples that illustrate what kind of damage can occur. There is impact damage as a result of foreign objects like a stone or a bird strike which results in a matrix crack, a crack perpendicular or horizontal to the surface. There is fibre breakage as a result of heavy loading on the object which is caused through severe tension on the fiber. Delamination is the lack of adhesion between the stacked layers of carbon fibres. Delamination leads to reduction of strength an stiffness of the CFRP. Furthermore, different kinds of voids can occur during the manufacturing process. Voids exist in all forms of composite with variations that depend on the fibre’s structure and density. This can affect the mechanical and electrical performance of the object. All these kinds of defects have to be noticed in a very early stage to ensure the reliability of the material (Lin,
X., 2012).
Figure 4: Forms of delamination (Menana, H.,11 Fliachi, M., 2009).
3.4 Skin Effect & Skin Depth
The minimal tested thickness of CFRP was 0.25 mm and highest tested thickness was 3.1 mm in this thesis because of sample limitations. When eddy currents are produced in a conductive material as CFRP the currents will not flow uniformly through the component (Lin, X., 2012). An important characteristic is the skin effect. The skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. Finally, at greater depths the eddy currents would not have any effect at all and become negligible (Lin, X., 2012). This is where another characteristic will be introduced: the skin depth δ. The skin depth is defined as the depth below the object’s surface where the intensity of the eddy current is reduced with 1/e, so reduced till ± 36.79 percent. When the reduction of 1/e is obtained it is called the standard penetration depth δ for the specific material. Where e is Euler’s number. The formula for the penetration depth is given by equation (5) (Full derivation in appendix) . The frequency f in [Hz], the permeability µ0 in [H · m−1] and the electrical conductivity σ in [S · m−1].
δ = √ 1
πf µσ (5)
(Full derivation in the appendix)
The electrical conductivity is constant at a specific frequency and the permeability is µ = µrµ0
This results in skin depth δ in [m] that behaves as a function of the testing frequency, f . The values of σ and µ are typically 0.01 · 104− 1.5 · 104 [S/m] and 4π · 10−7[H · m−1] (Lin, X., 2012).
The thickness of the plate must also be taken into account. Only when the plate’s thickness is more than three times the δ-value there is no distortion of the eddy current distribution. When the plate is thinner than 3 times δ the distortion can change the impedance that will be measured (Lin, X., 2012). This can lead to a good method to investigate how thick the measured object is, which can verify the given thickness of the plates that are used (lift-off effect). The CFRP plates that have been used in this research are not even close to the thickness of three times δ.
The aim of this thesis is to determine the quantitative penetration magentic fields of specific CFRP plates based on eddy current testing concepts that work well on metals. To do this, lift-off effect, skin effect, orientation of measurements and frequencies must be taken into account to determine the skin depth and investigate how the magnetic fields penetrate the material. When the penetration is deep enough, eddy currents can be used as a method to investigate if the CFRP material has cracks and flows.
In order to do this, the penetration depth must be linked to the change of magnitude of the magnetic field. This is detected by the coils. Therefore formula 6 links the electronic measured magnitudes to the penetration. First one has to make an approximation that describes the change of magnitude to the thickness of the carbon fiber plates as shown in formula 2.
V V0
= e−α·l = e−lδ (6)
Here the α is the coefficient that describes how the magnitude falls as function of thickness of the plate l in meters. V is the measured voltage when the magnetic field is interrupted by the CFRP in volts. V0 is the original voltage when the magnetic fields in not interrupted.
Equa-tion 6 is now written in terms of σ. Formula (6) rewritten as funcEqua-tion of the approximaEqua-tion of the skin depth:
δ = −l log(VV
0)
(7) However, account must be taken of the fact that the value of the magnitude is not measured in volts but in decibels. So δ becomes:
δ = −10 · l log(10) · VdB
3.5 Conductivity
Now there is a quantitative approximation of the skin depth δ of the CFRP plates. The other values f, π and µ0 are also known. This gives the opportunity to calculate the conductivity
due to the approximation of δ. Menana & Fliachi dirived a theoretical model in 2009 about the skin depth to give an upper and a lower limit of the conductivity to calcultate the skin depth (Menana, H., & Fliachi, M.,2009). In this thesis the conductivity values are choosen between 0.01 − 2.0 · 104 [S/m]. The only unknown parameter for equation (5) is the conductivity σ. This means that by quantitatively determining the skin depth δ the σ can also be calculated. Equation (9) shows a reformulated form of (5).
σ = 1
f · µ0· π · δ2
(9) In 2010 Nurul et al. discovered that when using lift-off scans with eddy currents, the conductivity increased with respect to the increase of the frequency (Nurul et al. 2010). The NDT research centre of Iowa State University also described this effect that increased frequency led to an increased conductivity value (NDT Research Centre, 2014).
4
Method & set-up
4.1 Equipment
In this thesis the Analog Discovery 2 (AD2) from Digilent was used to analyse the amplitude in dB and phase shift as function of the frequency f . The Digilent AD2 is a USB oscilloscope and multi-function instrument that allows users to measure, visualize, generate, record, and control mixed-signal circuits of all kinds. For details see the Analog Discovery 2 manual (Analog Discovery 2TM Reference Manual, 2015).
The coils that were connected to the AD2 were Texas Instruments EVM coils. In this research the used was the coil H: 46mm in diameter, 50 turns, 6mil trace, 6mil spacing, 2 layers thick. This coil has a self-resonant frequency of 2MHz. For more details see the Texas instruments User’s Guide (Texas Instruments LDC Reference Coils Users Guide, 2015). The program ”WaveForms” from Digilent was used to measure the magnitude with corresponding frequencies. The network analyzer drives a circuit with a swept sine wave up to 10MHz (2MHz was used), and measures circuit response as the input frequency changes. Output magnitude and phase are displayed in Bode, Nichols, or Nyquist formats.
6K Twill Weave CFRP with different sorts of thickness are used as test composites. The samples are 4x4 inch of standard 2x2 twill sheets. The thickness of the CFRP samples were in the dimensions 0.25mm, 0.5mm, 1.0mm, 1.3mm, 1.7mm, 2.4mm and 3.1mm. (The plates are made at Protech composites). Furthermore, Matlab and Python were used to analyze, calculate and fit the data.
4.2 Measuring method
To measure the change of magnitude an oscillating magnetic field must be generated. As one can see the AD2 (right) in figure 2 is wired to two parallel air filled coils. One of the coils is transmitting, the other is receiving with a changing frequency. Now the CFRP plates can be placed on by on between the coils as one can see in figure 3. When the oscillator has started it measures 1000 datasets for each plate each at a different frequency. The frequency that have been used are between 20 KHz and 2MHz at a logeritmic scale. Furthermore, the measurements were performed on all seven plates on both sides of each plate. The measurements were performed on both sides because this exchanged the role of
the transmitter and receiver coils to minimize the difference between the CFRP sides and to minimize the difference between the left and right coils.
Figure 5: Texas Instruments coils in green on the left. The Analog Discovery 2 on the right side in the figure with wires connected from the AD2 to the coils. Between the coils is a gap where in between the CFRP plates are placed.
5
Results
5.1 Magnitude scanning
In this section the figures 7 and 8 show respectively logarithmic scaled frequencies and linear scaled frequencies and their corresponding voltage magnitudes measured in dB. The data obtained from these figures showed that thicker plates led to a decreasing in magnitude of the measured voltage in dB. In the data, besides the decreasing magnitude, there is a self resonance in the frequency which starts at 1.2 MHz not at 2 Mhz what is said in the manual. There is a peak value that shifts to the right in both figures when the plate thickness increases. Both these results will be discussed later on. There is no difference between the left and right side of the plates during the measurements. There is also no orientation difference when rotating the sides 90 degrees. This will be discussed later on.
Figure 8: Linear scaled frequency in Hz with magnitude in dB. Legend labels the plate thickness.
5.2 Skin depth results
From the datasets obtained from the measurements, it is possible to calculate the skin depth by filling in the values obtained by the approximation. For every frequency between 4·105−10·105
Hz the skin depth has been calculated as equations 5 - 8 describe. Figure 9 shows the skin depth in m as function of the frequency [Hz].
After the transformation noise occurs in the signal with the 0.25 mm and 0.5 mm CFRP plates in the beginning of the measurements at lower frequencies. The other graphs all follow the same decreasing trend as the frequency increases. Also, all the graphs show a little trench in the middle of figure 9 between 7 to 8 ·105 Hz which will be discussed in section 5. Additionally, Figure 9 shows that the skin depth behaves as √1
f. Furthermore, Table 1 shows
the penetration depth at 5.0 · 105Hz for the different CFRP thicknesses and their penetration depth to show the order of depth. The order of skin depth is between 1.83 cm and 0.55 cm.
To ensure the system’s offset has nothing to do with the results, figure 10 shows how the penetration decreases as function of the plates’ thickness for different frequencies. The steepness of the slope gives an indication how deep the eddy currents penetrate the surface. Higher frequencies show steeper decreasing slopes than the lower frequencies. The three middle measurements, 1.0 mm, 1.3mm and 1.7 mm show for all the frequencies a higher value than the least squares line that runs through the measuring points. The first two and latter two are lower. This will be discussed in the next section as well.
Figure 9: The skin depth as function of the frequency for different CFRP plates. The legend labels the plate thickness.
Figure 10: The CFRP plates with different thickness are plotted against the magnitude in dB. The higher the frequency steeper the slope. Legend labels tested frequencies.
plate thickness [mm] penetration depth [m] 0.25 0.0183 0.5 0.0183 1.0 0.0146 1.3 0.0132 1.7 0.0108 2.4 0.0067 3.1 0.0055
Table 1: Table of the penetration depth values for different CFRP plates in meters at 5.0 ·105 Hz.
5.3 Conductivity results
Figure 11: The conductivity of the CFRP plates are increasing when the frequency increases. Legend shows CFRP thicknesses.
From the data that is obtained from all the previous results the conductivity can be calcu-lated using equation 9. Figure 11 shows how the conductivity increases when the frequency increases. Furthermore, Figure 11 shows difference in the plate thickness shows a different trend in conductivity increase. The 3.1mm plate has a significantly higher conductivity than the thinner plates. Tabel 2 shows the conductivity increase for the CFRP plates at a frequency
of 5.0 · 105 Hz.
Plate thickness [mm] Conductivity [S/m]
0.25 1.5165e+03 0.5 1.5079e+03 1.0 2.3755e+03 1.3 2.9029e+03 1.7 4.3581e+03 2.4 1.1414e+04 3.1 1.6555e+04
6
Discussion
The behaviour of the skin depth that was shown in Figure 9 was expected. The frequency increase led to an decrease of penetration through the CFRP. This meant that the skin depth also decreased if the frequency increased. In Figure 9 there is a trench between 7 − 8 · 105Hz in all the plots. This decrease is probably caused by the self-resonance of the wiring used between the AD2 and the coils or the electrical circuit of the AD2 systemboard itself. The peak occurs at 1.2 MHz. The Texas Instruments manual gave 2.0 MHz as self-resonance. Non of the measurements after 1.2 MHz have been used in this thesis. The skin depth result showed that there was noise in the smallest two CFRP’s at lower frequencies. This noise was caused by the precision of the measurements and the measurement equipment. The very small numbers fluctuated to much in the beginning to yield a smooth graph. In Figure 10 I could not explain why the three middle points for each least squares lines were higher than the fit analyses. Maybe because there is no real linear offset in this way of measuring. The coils were tested both ways. The CFRP’s were in two identical sets who gave almost identical values and the results are close to the theoretical values. So eddy current testing shows great opportunity to become very useful in detecting cracks and flaws because the quantitative penetration is large enough to see through the material. Magnitude scans a fast and cheap combined with the suited penetration in the material it will probably be a good method to replace expensive DT methods. The length of the gap between de coils is not relevant because the V and V0are relative measurements. The limitations of the equipment and measurements
during this thesis have no significant impact on the results.
As can be seen in figure 11 the conductivity depends on the alternating frequency. This behavior was unexpected because the conductivity of e.g. metals is not strongly dependent on frequency. The effect that was shown in figure 11 was later confirmed by other research. This effect was not expected in advance. Follow-up studies could explain the conductivity behaviour.
All the cracks and flaws noticed in this thesis are defects in a perpendicular direction. Defects perfectly aligned in the direction of the D-field can not be detected.
7
Conclusion
What is the quantitative penetration of eddy currents in CFRP plates? By performing quan-titative penetration measurements of eddy current testing on carbon fiber reinforced plastics and the theoretical model it shows that the penetration is between the 0.5 cm at 1.0 MHz to 3 cm at 10KHz. In the quantitative analyses for penetration and skin depth of CFRP’s, the measured values are close to the theoretical values. Namely 1.46 cm for 1.0 mm thickness to 1.32 cm for 1.3 mm thickness at f = 5 · 105Hz. Additionally, the results show that eddy
cur-rents can be used as a research method because the magnetic field significantly penetrates the plates to see through the total thickness of CFRP materials used in automotive and aviation industries.
For performing quantitative analysis of the the conductivity, the σ behaviour corresponds to the literature but was not expected in advance. Taking this all into consideration, quanti-tative eddy current testing shows that as the alternating frequencies increases the skin depth decreases and the conductivity increases.
Follow-up studies have to investigate the reason behind this behaviour of conductivity on CFRP. Also the orientation of the Twill weave fibers had no impact on the result but literature explicitly noticed the anisotropy in CFRP. During this thesis there we no effects at all.
8
Acknowledgement
I would like to thank Rudolf Sprik in particular. Rudolf told me about this subject and gave me some very useful ideas. He guided me when necessary and opened a spot at his desk at D-lab at the VU to run tests en finish my bachelor thesis. Rudolf also gave me the freedom to make it my own research which I appreciate.
I would also like to thank Sjoed van der Heijden for his interest, time and patience dur-ing programmdur-ing in python at D-Lab and write some codes.
Finally, I would like to thank Davide Iannuzzi for also giving me the equipment and space to do research at D-Lab.
9
Bibliography
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Appendix
The next page contains the the full derivation of the skin effect and skin depth. Derived by Kevan Hashemi, 2014 Brandeis University, Brandeis University High Energy Physics. This derivation is taken up in the appendix because it would not fit in the thesis lay-out.
